I would venture to suggest that Tonga is not north east of the Cayman Islands....
I confirm ! I made a stop there on a travel between New Caledonia and Tahiti . I don't remember the name of the town (not easy one) but I still have the plate received from the Tongian Navy ship who was in charge of us.

By the way, I've never sailed the Carribean sea
The mystery ship is a nice looking fishing boat as travel home
Xtian