Is there a way to stop the game timer advancing while not logged in? Frustrating to get ahead before bed, only to see Rome with 8 cities (from 1) next door to me when I wake up.
The production not shifting is the point of the building. That is if the large temporary boost is less than your previous boost its production doesn't change because it retains the highest temporary boost even if they wear off.
AI should only be active if the game is running. Also if you pause the game before leaving the game, it should remain paused until next time you play