I have observed that stone hatches, whether hatched in the incubator or left to hatch on their own, do not have a baby phase and are fully adult as soon as the egg hatches. Sage hatches, however, DO have a baby phase. This seems like a bug so I figured I'd let you know.
Steps to Reproduce
Hatch a stone hatch egg.
This issue has been fixed in either a future version or updated in a previous version.