Can you get actions in another players turn with Hidden Ninja and Chronomage?
In the "Void Where Prohibited" section of the rules it says "If you get to play extra minions or actions while a base is being scored, you must play those extra cards immediately or not at all" which means that you DO get to play the extra card from the Chronomage, but only if you play it immediately.  You can't wait to see if other cards get played first.

While it may seem weird to be able to play actions during other people's turns, this ruling has been confirmed by an AEG rep here.