This is only my opinion but since I do a lot of reading it is my conclusion that the influx of cruiseships to Jamaica did not unduly influence the crime problem.
I think it actually germinated many years before when hotel chains and investors started building those all inclusive resorts to which you have to fly. They wouldn't buy nary a thing from the locals, preferring to import virtually everything from the States even though a couple of these mega resorts were I believe British owned. Some wouldn't even hire the locals most of whom live in squalor outside of the resorts.
That is definitely not the way to build "good will" or offer even a modicum of support to the country or island on which you wish to do business.
NCL Epic 2012, Eastern Caribbean
Explorer of the Seas 2009, Eastern Caribbean
Explorer of the Seas 2007, Eastern Caribbean
Explorer of the Seas 2006, Eastern Caribbean