On the western itinerary, the ship's clock is set back one hour between Grand Cayman and Cozumel,
unless you are sailing during daylight savings time, in which case it is set back an hour between Key West and Grand Cayman. Grand Cayman is in the eastern time zone, but does not "celebrate" daylight savings time. Cozumel is the the central time zone, and does use DST. In both cases, the clock is set forward an hour between Cozumel and
Castaway Cay.
On the eastern, it's set forward while at sea between Port Canaveral and St. Maarten, then back again between St. Thomas and Castaway Cay, but only during standard time. During dayling savings time, the ship's clock, at EDT, is the same as Atlantic Standard Time, which is used year-round at St. Maarten and St. Thomas. Both are far enough south that they don't need daylight savings time.
No changes on the 3- and 4-day cruises, as the Bahamas and Florida are in the same TZ.
In other words, the ship's time should always be the same as the local port time.
Hope this made sense. Dave has a better description of all of this at
http://www.dcltribute.com/faq/timechange.htm.