The island on the continental shelf of South America which include Trinidad and the Abc islands are in South America while the rest of the Caribbean is considered part of North America
As you can see in the map the Caribbean is considered part of North America.
You can see Trinidad and Tobago included in the map.
Though on the map theres a number key showing that parts of the Caribbean (Dominica, St Lucia etc) can be considered in South America. There isn't really a defined rule.
The Caribbean has its own plate, the Caribbean plat though because its small its not really considered a real continent (and it isn't)