Ship time is the one that is important. Whatever the time zone the ship departs from determines that. So, it really doesn't matter what the island time is, if the ship sails at 4 then it sails at 4 ship time, even though island time may be an hour different.
When we sailed last April were were on DST. We sailed from Tampa to Grand Cayman, Costa Maya, Cozumel and Belize. Grand Cayman, Costa Maya, and Cozumel were all an hour behind us and Belize was 2 hours behind. I brought a cheap watch with me and set it to local time and kept my wrist watch set to ship time so I always knew what time it was in both places. This way I made sure we were back in plenty of time to catch the ship. Hope this helps.
Celebrity Century 1/09
Carnival Destiny 10/07
Carnival Destiny 9/06
Monarch of the Seas 3/06
Carnival Inspiration 8/05
Carnival Miracle 4/05
Carnival Inspiration 4/04
Sovereign of the Seas 4/03
go by the ships time. I know that on Princess they put a little card on your pillow the night before and tell you to set your watch forward or backward accordingly for the next day. The important thing to remember is to be be back on board the ship 1 hour before departure - Ship's time.
All you need to do is ask your tour operator if local time is 1 hour or whatever ahead/behind ships time - they will know - their business depends upon it.