zackish, the babies are most likely not baby mystery or apple snails. Apples reproduce by laying big blobs of bubble-gum looking egg clumps up out of the water, then these eventually hatch and the babies fall back into the water. You might check up under the lip of your aquarium though.
What you're seeing is most likely a pond snail or some other more common freshwater snail. I love 'em, but some people don't like them. They don't cause any harm though, at least I claim they don't and I've had them with just about every soft-leaved species you can think of.
I've had mystery snails in a planted tank before, and they did dig a little. So far I can't say they have hurt my plants at all though, and it's really fun to watch them cruising around.