If I terminate an employee in HotSchedules, will this automatically remove them from the POS system?

If you are an integrated site, the only way to ensure the removal of a terminated employee is to terminate them from the actual point of sale system first. If an employee generates on the staff list again, then they are still active somewhere on the POS. You can test this out by terminating them out of POS and then running a manual sync from the back of house, main computer OR wait for the normal overnight sync to go through.