Jamaica is a constitutional monarchy under the British crown. It would be a gross oversimplification to call all of these nations puppet states to the US, ignoring a lot of their own colonial and post-colonial history. Much like mainland Latin America, there are influences from England, Spain, France to varying degrees in the region.

Of course, the US views the Caribbean as its “backyard,” and has intervened a ton throughout the 20th century, like the invasion of Grenada in the 80s.