The Digicel store Megamart in Mobay refused to sell me a sim card.
She told my she can't sell to foreigners and then said a Jamaican ID is required.
Not sure if this has changed but others have posted similar problems with getting a new sim at Megamart.
After a few days without a phone, I got a loaner sim from a driver.
Kinda a pain in the A$$ as I loaded a ton of info into it and couldn't use it right away...

Again, this may have changed since April...