The time starts in the time zone you depart from. Then the captain can "choose" to adjust the time if they are cruising to place with different time. If they choose to remain on the time zone from which the ship departed from; they will tell you to stay on "ship's time" while in port and ignore the local time. This is VERY typical in the caribbean when sailing to Mexico as Mexico does NOT have day light savings; we are typically an hour off from Fort Lauderdale and therefore the Captain can choose to have you set your clock the night before (at 2am) to the new time of the port prior to docking or ask that you stay on "ship time". It's entirely up to the Captain. For example, I sailed on both Allure and Vision this year; both ported in Cozumel. Allure asked that we all stay on Ship Time; while the Vision captain asked we set our clocks back an hour. It just depends on the captain.