Blowing into a cartomizer that is in a tank will create pressure in the tank which once the blowing quits means that pressure will equalize, if there is liquid at the holes going into the cartomizer it will simply push more liquid into the already over saturated filler. I like to use the refilling drip tip to lower the cartomizer holes below the bottom cap then blow it gently into a paper towel or simply vape it down while it is in this position where it cannot get more liquid inside of the cartomizer.
The other thing as Andria noted is vaping through it. The important thing here is understanding the mechanics of how the liquid is coming into the cartomizer. I say this because by varying the style in which you vape you can change how much liquid is pulled in. A short hard draw will pull in more liquid than a long light draw as far as the ratio of time on the button spent atomizing per volume coming in. I have also seen a lot of people with flooding problems due to what I would call a kindling habit, you know when a cigarette dies down or a pipe or cigar had gone to ember? Well it would take a few short puffs to get it going then take that draw. With a cartomizer tank though every vacuum/equalize cycle draws liquid into the filler regardless of how much is being atomized and removed so the longer you stay on the button and the lighter draw with its lower vacuum the balance will tip away from too wet.
Same ideas at work here re popping the cap off to fill. When you do that the cap acts like a piston building pressure in the tank, that pressure will push the liquid from the tank into the filler and of course out all over the place if the filler is already saturated.
My preference if for the thingy method of filling. It is just too easy and clean. You are correct in that the top of the filler doesnt need to look wet. We only sell single coil cartomizers because they make sense in a tank, a dual coil will have one up higher than the other meaning the wet level needs to be higher to keep it from burning with a single coil you have more range in just how wet the cartomizer is that it will vape fine in because the coil is down in the bottom. Very important not to put too much power to a cartomizer until you are certain there is liquid in contact with the coil, thats the idea behind the short taps on the power button while taking a normal full draw. Those draws will pull the liquid to the center of the cartomizer where the coil is and the short pulses of power will prevent it from getting hot enough to scorch. Once the liquid is to the coil the conversion from liquid to vapor will pull that power off.
I am guess you have the 19mm Tank because yes the inside and outside orings are very close to each other. If you look closely though two of them are a slightly larger diameter and a little thinner than the other two. Those are the inside orings. The inside orings for all of our caps are 10.1 x 1.6mm and the outside of the 19mm caps are 9.5 x 2mm so you can see there is enough of s difference to discern by eye but you have to compare them to each other to spot it.
Most often when I found a "catch" with the refilling drip tip it had been from tilting it over while sliding the cartomizer through. You want to hold that top cap while inserting the cartomizer so your fingers can kind of get into the way so thats something to watch for. I personally dont have any other tank tool and dont feel the need to though there are others that many have posted that are better quality, they of course are not $2.50 so that is a consideration.
I hope you can get things sorted because I have found cartomizer tanks to be about the best vape for the least amount of fuss. Cartomizer tanks certainly are not for everyone but if you can find that balance of vaping style and hardware that suits you it will quickly settle in.