The Caribbean is North America. He landed in Cuba and on the island of Hispaniola.

Yes, but he still instigated the events that lead to the colonization of the americas, north america included:

Columbus's expeditions inaugurated a period of exploration, conquest, and colonization that lasted for centuries, thus bringing the Americas into the European sphere of influence. The transfer of plants, animals, precious metals, culture, human populations, technology, diseases, and ideas between the Old World and New World that followed his first voyage are known as the Columbian exchange, named after him. These events and the effects which persist to the present are often cited as the beginning of the modern era. ^(^^source^^)^