At the risk of sounding like Yogi Berra, they probably immigrated to St. Kitts because there were other Huguenots there. There were early groups of them and, as C. Handy suggested, it's easier to hide further from the French crown.
I know that were was immigration from St. Kitts to colonial Virginia, too. While I'd bet that there was an element of pursuing economic opportunity, there were Huguenots in Philadelphia, some of whom they have known.
It was probably easier to make the move, too, given that the hostilities between Great Britian and France had ended.
P.S. You might look at the Huguenot community in Philadelphia and see if there were relatives or other people from the same communities in which your family originated.