Should the snails grow up on their own to large state? I see many snails that are full grown wandering about, I thought they needed to be cared for to grow large?

They should never grow up on their own, if they do it's a bug. In all of my extensive testing I was never able to notice such behavior.

Please check if they are tamed and their satisfaction level in NBT.

Hmm seemed to be an issue with an old world having it installed I tested on a new world and spawned a ton of them. They dont seem to be reacting the same way now. Strange.