Sometimes you want to move a character to a different floor to avoid one of the others being discovered - because the guard on the floor they end on is the one who moves.
Definitely the move is after each character goes.
Spreading out between the different floors is key. And often times you get one player stuck on a floor unable to move up or he'll end up causing guard to catch another player. Not super sexy for them but it's hard being successful burglars.