Here is the thing with the terminology when it comes to the Caribbean.
The Caribbean refers to the island archipelago that extends from Cuba all the way to Trinidad. The Netherland Antilles are technically not part of the Caribbean island chain, but they are included non the less. The same applies to the Bahamas, The Turks and Caicos, even Bermuda (out in the Atlantic Ocean somewhere) is often included under the name "The Caribbean".
That's why people can say that they live in the Caribbean even if the sea washing upon their immediate shore may be the Atlantic Ocean. The idea is that the islands are part of the Caribbean more so, than the Atlantic Ocean. That's why Escott and many other people say they live in the Caribbean, even on the north coast of the Dominican Republic.
While I'm at it, another thing to keep in mind when refering to Geography is that North America the Continent extends from Alaska to the Panama Canal and includes the islands of the Caribbean but excludes Hawaii. However, when people talk about "North America" that only pertains to Canada and the USA (including Hawaii) and also Mexico (known as North America's Deep South due to it's economic malaise). Mexico is also known as an NIC or Newly Industrialized Countries meaning, in technical terms Mexico is not considered poor anymore. That is all technical, reality is a different story of course. Also, Central America officially is a sub-name for the isthmus extending south of Mexico but north of Colombia and includes the islands as well. But, in general terms, when people talk about Central America or Banana Republics, they usually are refering to the isthmus excluding the island which are general known as "The Caribbean". South America is known like that in official and general terms and it's the entire peace of land south of the Caribbean.
Also, (once I start is hard to stop but I must say) Anglo-America only pertains to the USA and Canada. Latin America only pertains to countries in the Western Hemisphere that at one point were a colony of a Latin based country (either Portugal, Spain, France or Italy). So, if a country speaks spanish, portuguese, french, or italian and still has a significant influence from it's mother country it's consider part of Latin America.
And (this is the last one, I promise) the word Hispanic pertains to people that either come from or are decendents of Spaniards. Hispanic derives from the Latin name of Spain which is Hispania. The island of Hispaniola (where the DR is located) means the Spanish Island or the island that belongs to Spain. A Latino is an American name for anyone that comes from Latin countries in the Hemisphere (excluding Portugal, Spain, France, and Italy) and as promised, that is it. For now at least.