Most items purchased in Jamaica are duty free, but some have limits. For example you are allowed two bottles of rum per person . If from the States , Cuban cigars are still not allowed. You may buy them & smoke them there,however. On some shopping tours they will take you where items are duty free. Just be sure to ask if you are not sure. Customs in Jamaica are pretty much the same as other places. On your departing flight ,going through customs they may choose to check your luggage. Don't be alarmed. They look inside purses , and carry ons and it is best to also have your pockets emptied before you walk  through the detector.