This is a bit late but I'm going to reply anyways for future and other people's benefit.
My primary experience with snail eggs is with the related, larger species of apple snails (pomacea canaliculata) but care should be similar. Apologies if any details are less necessary, but you still can't go wrong.
Leave a bit of space at the top without water (it looks like it's above it?) This would be especially important if there's someone willing to eat them in there, including larger snails. Not sure about bettas. Mystery snails are pretty harmless but their larger counterparts sometimes eat their own eggs if they aren't fed properly or feel like it, so make sure they aren't hungry. Daily softly splash a little water on them to keep them hydrated, or they might dry out. And wait!
Otherwise there's nothing to do. As for the tank size, probably either (1) coincidence, (2) water better regulated, (3) subtle changes in diet more-so related to the inhabitants than the size.
