Yes the wick goes into the cups.
Thats why depending on thickness you need to modify the amount of wick in the cup and how close ou place it near the opening.
THin juice the wick legs will need to have it closer to the hole to keep it from over wicking and thicker liquids need a bit more space from the hole.
You can see my wick tails thru the holes if you look, I use 90 VG or more. I also do not have such thick wicks as you see. If you have thinner liquid than your wick tails will need to be stuffed thicker in the cups and maybe around it too. Its a matter of a little minor adjustments to suit your liquids and ambient temp.
I am in a home that does not have AC so I have to use a bit more material this time of the year. I also use a smaller diamter coil so I dont get gurgles. In cooler weather I can use a larger diameter coil etc.
Maybe some of you are using thinner liquids with too large diameter of coils? To keep the liquid from over flowing youd have to jam those wick holes/ cups with just enough material to keep it from going dry and flowing.
Disclaimer, this photo was done for a friend, so I have no idea if it had problems, Probably just by looking it would or might leak as that is a FAT coil and probably would need more wick material to keep it from flooding..
My wicks look just like that but with a single 28g SS wire, at 2.4 diameter coil.