found this on CC:
Okay, some clarification here. For MOST normal Caribbean cruises (not Panama canal, not Alaska), ship time will remain the same throughout, namely the time zone applicable during embarkation (let's say EST out of Mia in the winter). That clock won't change onboard. And all the information you receive (like when you need to be back to the ship on a port day) will be reflective of that original ship time. As others have said, that may not coincide with local time in any individual port. That said, the private tour operators do this every day and understand the conversion. Any communication you have with them beforehand can clarify any differential between the two. And it's always good to check with your tour operator during your tour.
Here's an important thing to remember. Do not rely on your cellphone to be accurate with respect to ship time once you set foot ashore. There is no substitute for a good wristwatch set to ship time during the week.