No name LR cartos? Hmm.
I know that Boge LR cartos are arguably the "standard". I find Boges are great out of the gate, have tightly packed filler, and tend to stay loose on the draw the longest.
Smok cartos have a looser filler, which works well for my thicker juice. They do tend to tighten up faster though, and draws become tougher faster than the Boges. This is across their entire carto line, DCC 1.5's, 1.7's, 1.25's, etc.
I've read (no firsthand experience) that Kanger cartos have a "different" taste. Whether that's the filler, wick, primer, is much debated, but they generally taste different according to a lot of people.
What juice are you using? Atties will inherently give better TH than a carto, but a good LR carto will give a nice amount of throat hit. Also, what battery is all this run on?
The juice pouring out the bottom could be just overfilling. If it's a Boge sized carto, you're looking at 1ml-1.5ml max of juice on the first fill. While syringe filling is normally uneventful, you can try both the condom method or drip fill it to see if the filler absorbs the juice without leaking. Make sure you blow out the carto a little if you hear juice gurgling on the draw. The "sizzle" is normal usually.
And yes, some cartos do need a break-in before hitting their taste peak. I find that my Smok 1.7 SC's taste ever so slightly burnt when first filled (and I'm an obsessive compulsive filler, syringe fill, thermometer shakes, waiting 30 minutes, etc.) but really hit their stride after the first ml of juice.
Report back. Let's get your cartos working properly.