If you switch to day at night and they are exhausted, they will be exhausted/tired for a little bit (maybe take some naps), but they'll perk up pretty quickly and will do normal day activities
Then it'll change to night time when it's supposed to be day time based on your time zone.
As for pausing, I'm not sure of the logistics, so someone else might want to chime in, but it sometimes causes a time delay as the game tries to catch up.