Ok, funnyfarm... you've only tried just the one carto (I'm assuming its a smoktech dual coil at 1.5ohms, since that's usually what comes in those tanks) on it, right? Did we ever establish how many holes were close to the base of your carto inside the tank?
If its more than 1... that's your problem, right there. The cartos that have more than 1 hole prepunched tend to be best for thicker juices, like an 100% VG, thicker blends.
If its only one... the only thing I can tell you is that occasionally those 'prepunched' cartos have the same issue as the ones you punch yourself using a carto punch or a saddle valve. I'm not sure what the issue is, but I suspect that occasionally the hole breaks through into the center tube of the carto, or else is just way too big, so you get a ton of juice with your vapor. Another option, and this was the case with my friend... he actually disassembled his carto (after our troubleshooting established that the carto was funky) and found that he'd managed to MELT the inner plastic tube that keeps the juice away from the vapor hole. That was why he kept getting tons of juice in his vape. We suspect this is cause it was a dual coil, and the plastic down by the coils just melted. Another reason I like single coils in tanks. lol But for your situation, first thing I'll tell you is stop vaping with that thing! Nic levels in eliquid are safe, assuming you're getting them from a reputable vape shop, but you're not supposed to drink the juice! lol If you get any in your mouth, spit it out immediately and flush your mouth with water. I'm not expecting you to have any serious adverse reactions, cause you'd have to drink quite a bit of juice to run into nicotine poisoning issues, but nicotine is a stimulant and can cause your heart to race, and also virulent hiccoughs (hiccups) that last for hours... trust me, I've been there. But the bad news is that if the one carto that came with your tank setup isn't working properly, there's not much you can do to fix it. I'm not 100% certain its a bad punch, but that's what I suspect. If you're willing, we can do a little bit of troubleshooting to find out once and for all if the carto is bad, or if you just did a bad fill. This will take a little time and effort, though. Lucky for you, this just happened to a friend of mine so I had to figure out how to start fresh with a new fill to see if the carto was the issue, or a bad fill. This is what I worked out for him.
1) suck up all the juice you can get out of your tank with a syringe, and put it back in the juice bottle for now.
2)next step is to get the juice out of the carto. The quick way is to try to suck as much juice out as you possibly can with the syringe (I should have mentioned, you need the carto out of the tank for this part... which is why you took out the juice), simply by sticking the syringe all around the filler and sucking out as much as you can. This is less effective than using the 'reverse taryn spin' method to get the juice out. You can see a video on how to make a 'taryn spin bag' and do the basic taryn spin method here. This method is the best way (in my opinion) to fill filler cartos that you use outside of tanks for the first time, to get the longest life and best vape out of them, so its useful for other things, after this trouble shooting session. After you fill a carto with this method on the first fill, all you have to do from here on out is just drop 4-5 drops of liquid on the filler every few hours, and it will continue to vape great for weeks and weeks. And making the bag is a little hassle, but you only need to make one every 6 mos or so, and reuse it again and again. Instead of the long lanyard, i use two zip ties connected end to end to make a small loop, sliding it thru the 'holes' on the baggie before you connect the last two end together to finish your loop. That way you can just do a tiny spin around your finger, rather than the whole lanyard loop, but that way works just fine, as well. You can also use a $1.50 velveteen pouch w drawstrings to hold an ecig for this part, you can get those from many vape places and use those instead of the homemade bags for spinning.
How To Fill A 510 Cartomizer (Electronic Cigarette) - YouTube
Ok, so after you watch this video, make your Taryn spin bag. THEN, Instead of doing the taryn spin to fill your carto, you want to do the 'reverse taryn spin' to get the liquid OUT of your carto. So you put the condom from the end of your carto (you might have to steal this from another cartomizer, since the ones that come in tanks don't come with those clear plastic condoms over the ends.) on the TOP hole of the carto, pushed about halfway down. You push only halfway down so that its secure on the top end of your carto, yet there is still room in the condom for the juice to collect. Put your carto UPSIDE DOWN in the spin bag, so that the top part of the carto, with the condom on it, is down in the baggie, and the 510 connection .... of the carto is up at the top. Boy, this is hard to explain in writing. Hope this make sense! lol Then you just want to spin your bag like crazy, until the condom is filled with juice. Pull carto w condom on it carefully out of the bag, dump whats in the condom back into juice bottle. Then repeat, putting empty condom back on the top of your carto, put upside down in bag, spin like mad, empty... until you've gotten all the juice out of your carto. Might take 3 or 4 repetitions to get all the juice out. And of course, since there IS a hole on your carto, because it was designed for a tank, you might get a little juice out of that hole as you're spinning. But don't worry... that's what the bag is for... to contain any mess. Just rinse your bag out and set it aside so its ready the next time you want to do the taryn spin to fill carto.
Ok, so now you've got a relatively empty newish carto, and hopefully a relatively empty tank. You're ready to try one last time to see if this will work. And it sounded like you have the general concept of filling the tank down, but here's how I do it. One thing you mentioned might be problematic, so try it this way.
1)So, put the carto back into tank, pushing it only halfway home, so that there's still room for you to get a syringe in between the top of the tank, and the outer wall of the carto, for filling.
2)Start filling with a syringe, right up until you get the tank about halfway full. You're not filling it all the way because we're not sure this will work. lol You might end up having to take the juice out again, if it turns out your carto is the problem.
3)Ok, now push the carto up into place, until the bottom plate fits flush against the bottom of the tank. Now here's where you might have gone wrong..its hard to tell from the way you described it.
4)Ok, what you want to do is fill up the carto by using a syringe straight into the filler material at the bottom, so the bottom of the carto gets filled up first. Then gradually work your way with the syringe up into the higher filler material, until you start to see the filler at top getting saturated. You can top off with a few drops on top of the filler if it looks like you need it. BUT at no point are you 'flooding' the top of the filler, hole included, with juice. That part is important.
5)Now you may want to set it aside for 10 mins, so the hole can fill rest of carto filler with juice and it can soak in. Now you can start vaping again.
Here's the bummer part... if you're STILL getting loads of juice in your mouth, than that carto is toast. Something went wrong with the hole punching part, and there's nothing you can do to fix that. You just need to either contact your seller, and tell him you followed troubleshooting directions at ecf exactly,and the carto is flooding center hole with juice... if you're lucky, he'll send you a new one, but that's not super likely. Many cartos have no guarantee unless they're Dead On Arrival, which yours is not.
Either way, you want to buy some new cartos for your tank, and were I you, I'd get a pack for use outside of your tank, just to be safe. Depending on the voltage you like to vape at, I like Boge 2.0ohm and Resurrector 1.7ohm single coil smoktechs for mid voltage vaping (resurrectors are also available bottom plated w 1 hole punched in em from
Crystal Clear Vaping. I've used MANY of his plated and punched 1.7ohm cartos, and never had one yet that was unusable out of the box, like yours) or the Boge 3s for high voltage. That would be an excellent thing to try if you're not into punching holes into your own cartos. I find punching my own a bit problematic. I certainly do it, but relatively often the hole will be too big, so I'll end up with the juice in mouth situation, which is what you're trying to avoid. BUT if you're comfortable punching your own, either Boge 2.0s or Resurrector single coils smoktech 1.7ohms for mid voltages or boge 3.0s at high voltages, BOTH IN THE XL SIZE, are excellent cartos to punch for use in tanks.
Ok, so not sure what you're gonna end up with after all that... let us know what happens! But unfortunately, some cartos with holes are funny right out of the box, so that whole troubleshooting brouhaha is designed to find out if yours is bad, or if you just flooded with filling. If you're not in the mood to mess with all that... if I had to guess, I'd say the carto is bad, unfortunately. Were I you, I'd buy a few of the 'punched and plated' 1.7ohm resurrector cartos in singles to try out in the tanks, and a pack of the Boge, either 2.0 or 3.0 in the XL size which can be punched in the future if you like, but will certainly work beautifully for you outside of a tank in the interim, while you figure it all out. If you've got a metal lava tube (like chrome/stainless/copper) with a loose draw, the unpunched 1.7om resurrectors are a great option for mid voltages, as well. I love the idea that some vendors are giving new vapers a tank in with their kits, but it can be problematic to troubleshoot them if you're not already super familiar with how carto work, ahead of time. My rule of thumb.... when you're new (and I don't know that you are, but try to write these things for a beginner to follow), and trying to stay off the cigs... aim for the simplest thing possible, till you get in the swing of things. Simplest for you, just for right now, would probably be a good carto out of a tank, while you figure out how to get optimal performance with the tank.

But now you've got all your options, and a little how to guide on figuring out whether your carto is permanently unusable, or just had a funny fill. Good luck! let us know how it goes!