Just incase you have not seen this, here is the official link to this cruise port: Home
A little history (if I remember correctly). The construction of the Grand Turk "port" was a join project by the country and Carnival Cruise Lines a few years ago. (It is very similar to "Costa Maya" in Mexico if you have ever stopped there (again built by CCL with the help of Mexico). It opened, I believe, the same year we visited there during our Regatta Cruise (see signature for date). The port is kind of a cross between a "private" island type of stop and a standard port-of-call visit. IMO, I would treat it the same as a private island stop.
Even though this port, as well as Costa Maya, were built with the help of CCL, other cruise lines do stop there, but CCL ships have first rights. Each have limited pier slots that keep the crowds well controlled, which make both of them excellent, and peaceful, ports-of-call.
(Again, I hope I have my history correct in my statements about this port and Costa Maya. Please correct me if I have misstated anything. It has been a couple years since I looked into this port.)