I never recommend that people do anything "local" in Jamaica. It is not a safe place. I really wonder why cruise lines even go there except for the appeal of the name.
Basically, it is worse than Mexico or any other place you have ever been warned about. Tourists are considered fair game.
The Jamaica tourism ministry is aware of the local problem but can't do anything about it as much as they try to explain to the locals that tourists means jobs & $.
It's too bad, because they island has the best name recognition in the Caribbean - but its one of the worst places to go.