The entire area is _supposed_ to use U.S. phraseology and procedures by LOA (an argument that was actually promulgated by FAA ATS management as a reason the U.S. shouldn't switch to ICAO terminology, you sort out that logic!), and if you look at the country differences, you'll see the local rules for each of the locations in the Carribean closely follow U.S. procedures. Sure, they're under ICAO, so is the U.S., but the U.S. publishes more exceptions to ICAO than just about any other country in the World.
Having flown both the area you're talking about and the "hard core" International on the other side of the planet, you're really talking apples and oranges here.