When does Cappy start saying if there’s anything left to do in an area?

Sometimes when returning to an area, Cappy will give a message telling you if there are any power moons or purple coins left in an area. If everything is collected, Cappy will say “there’s nothing left to do here”.

In order to answer Will Cappy tell me if there are purple coins left in an area?, I replayed Cap Kingdom and Cascade Kingdom on a new file. However, Cappy didn’t give me any messages about missing items when I re-entered hidden areas. (Presumably, I’d need to progress further in the story before getting hints)

When does Cappy start giving hints about missing items in hidden areas?

To prevent you from getting the notices too early, it seems that Cappy will only alert you of potential missing coins or moons when you've broken the moon rock for the kingdom.