What kind ATM troubles have been reported here?
ATM (ABM) is my preferred method of obtaining cash while in JA. I find that you get the best exchange rate and the fees are relatively low. Aside from that, I always keep my valuables in the room safe. Never had any problem with items disappearing from our room. Then again, we usually stay at places that have a staff of no more than 5 people, so if something is amiss in the room we have a good idea of who was in there.
Again, never had any issue with the ATMs in Negril. If security is a concern, then use the one inside Time Square. It's about as secure as an ATM inside any North American shopping mall. I also like the standalone one that is next to gas station by Rutland Point. The ATM at the ScotiaBank downtown can be annoying with the occasional beggar and random idlers watching you walk in and out, but often times they have a security guard standing outside the door. If not, you can ask your taxi driver to walk you to the machine and stand outside the doors.