I've never had any CC issue's in/from Jamaica in the 22 years I've been going.
Same for me. I call my CC company and I use my card at a lot of places, large and small, in Jamaica. This last trip I used it at two hotels, several restaurants, as a deposit on a scooter rental and a couple of shops (Hi Lo, Wise Choice).

I get travel rewards when I use that card and it has no international fees and it has a great exchange rate, so it's win-win-win. Also, I do NOT feel comfortable carrying lots of cash, or trying to keep it in my room safe or whatever.

I have had my card used fraudulently in the states...worst thing was not having the card for 5 days while they sent a replacement.

I never use my debit card for anything but ATM withdrawals.