Did you know that the baby won't start evolving until the Adult leaves to go back to Tama planet? (It sounds as though you might not from the way you have worded your post).
The adult leaves at midnight on the second night after the babies are born.
The next morning the baby wakes up on its own, you name it and as soon as you've named it, it starts to evolve and you're raising the next gen!
Best, etc.
TamaMum