The brand and franchise is what you see in Jamaica. I doubt that the food (chicken, french fries, etc) is not the junk franchise standard you would get in the US.
I believe all the chicken is local Jamaican grown. I can't imagine that the franchise is unloading an airplane or a ship to get their supplies.
The biggest chicken supplier in Jamaica is a company Jamaica Broilers.
The jerk chicken you get at any restaurant or barrel came from them most likely. Or did you think it was being raised in some yard?
It's good Jamaican food grown on the island and prepared by Jamaicans. Enjoy it!
Cap