I've worked on a ship. On US-flagged vessels, it is customary (probably even mandatory) to change the shifts when switching time zones. A one-hour change is normally broken into three 20-minute chunks, to distribute across the three watch shifts. There is a special board labeled 'advance clocks' or 'retard clocks' hung under the clock in the mess, so everyone is made aware.
During the month I spent on a ship in the arctic, crossing time zones every day, they stayed on a single zone. Of course, the sun never set, so it wasn't much of a problem.