Yeah that's not a good way to fill cartos.
You need to know the capacity of the carto. Juice dripping out the bottom how means nothing.
This is how I fill 1ml cartos but that 18 drops to start is per ml so that would be 36 for a 2ml carto, etc. You need to fill approximately to capacity with suitable juice, cleanup, then settle. For a reservoir carto the filling method would be different and settling would instead be just a wait for the wicks to bring the first liquid to the coils.
And I only use thin clear juices that flow and wick easily. In stuffing cartos I use PG w/ 20% or less VG (used to 30% which works but degraded my cartos faster than I liked). Reservoir stuff usually liked the thickness of 20-30% VG though thinner works (may leak more easily) and some thinner 50/50's may work. I avoid all juices that leave flavoring sediment behind (clogs cartos, gunks up attys).
NOTE - with bigger capacity stuffing cartos some people do use a syringe down the inner wall to fill the bottom to make sure the bottom gets wet. With thicker juices, people may use syringe or other method to make the juice go into the stuffing.
So this is for simple 1ml stuffing cartos but hopefully the concepts will help.
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How I fill Vapor4Life KR8 cartos and Boge 510 cartos
With the carto off the battery... Pop out the soft cap with an unbent paperclip in the mouth hole, very careful not to catch stuffing or the wire loop.
Shake and open the eliquid
Fill
Hold a bit of tissue on the threaded end hole, tilt the carto, and add 18 drops per ml of capacity into the stuffing (Boges and most KR8 cartos are about 1ml).
Wait 15 seconds or so then see how many more drops the carto stuffing will soak in easily.
Cleanup
Clean up the threaded end, tilt open end down into tissue, puff into threaded end to clear air channel (Boges and the KR8 cartos I use have a defined center air channel and I want to see light through that) While the carto is still open end down, touch a soft bunch of tissue to the top of the stuffing to get the loose juice - this will help prevent leaks.
Settle (first fill only)
Cap and let it settle - I lay it on different sides for 15-20 minutes to make sure every bit of stuffing gets damp so I won't singe the carto. if you use thicker juice than me (I use 20% Vg or less) then you may need to wait much longer.
While vaping
While vaping, if the vapor gets a bit light or a bit dry or the carto is getting hotter than normal, I take the carto off the battery and add eliquid. Also, I use such light sediment-free juices, I can look at the stuffing and see if it needs juice because the stuffing goes back to near-white.
I often use a plastic or delrin drip tip as a mouthpiece on Boge and KR8 cartos (not to drip into since the juice would head for the central air channel). Easy to pop out to add juice.