JimB is correct. You set your clock forward one hour on Sunday night and back one hour on Thursday night on the Eastern trip, when there's not daylight savings time. They do not recognize DST in the Caribbean, so EDT is the same as AST between April and October.
I haven't yet been on the Western, but I would assume that you'd set the clock back an hour on the night before Cozumel (assuming Grand Cayman is in the Eastern time zone, as its almost due south of Key West), and then forward again before Castaway Cay.
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