NY is part of the Tri-State region among which is CT (which is a part of New England). Maybe someone then assumed NY is too by law of transitive property / association.
You've been told incorrectly. Rhode Island is bordered by Massachusetts on the north and east and Connecticut on the west. It's southern border is the Atlantic Ocean. Long Island is part of New York, and doesn't even extend as far east as Rhode Island. Google it, check a map.
I’ve had this actual argument with someone. They first tried to tell me that New England was the original 13 Colonies and anything in the northeast. They didn’t even realize that the colonies included states like Georgia, the Carolinas, and Virginia. They’d never even heard of “mid-Atlantic” states.