I had not heard this rumor, and I tend to doubt that it is true. I would think that last year's cruisers would have noticed if there was a full-scale movie production on the island. Also, I doubt that the island could house the crew and cast while being maintained as a port call for
DCL.
The
Internet Movie Database lists St. Vincent and the Grenadines as the Caribbean location, along with Marineland of the Pacific, and LA (probably for the soundstage work) as the filming locations.