Does the Game Continue Even After You Have Quit the Game?

If you do not pause your game before you quit, several seconds (sim minutes) will elapse while quitting and while opening the save. The same thing happens when you go to change appearance in a mirror. While it is loading, time is still happening for several seconds.

Try pausing the game before exiting. That should take care of it. However, as others said, rotational play will work differently.