I think I should clarify my earlier post. On most Carnival Miami Caribbean cruises that I've been on the ship stays on Miami time. Dang!, I need to make sure what section I'm posting in.
When they moved the Elation in 2006 to Port Canaveral a week ahead of time before dry dock to do a cruise first, they did change the time for Cozumel. The Captain was used to doing West Coast runs, and apparently had the habit of changing the time for Mexico. As most know Port Canaveral has a large volume of repeat cruisers, and everyone was talking about how this was the first time it ever happened.
This get's better, this time change was also the same night Daylight Savings Time ended. The result was hilarious. No one knew what time it was including the crew. The ship's computers had one time and the public clocks had another. It really depended where you were on the ship.