You are always on ship time. Even if the ship changes its clocks for a time zone change you are still on ship time.
That said, I have done the Western Caribbean twice on Royal Caribbean on two different ships out of Miami both times. Both cruises went to Labadee, Ocho Rios, Grand Cayman and Cozumel. Both were during the summer (Aug 2004 and June 2007) and we never changed the clocks (ahead or back). However, we were always on ship time.