Using a sharp knife, cut slits into the pork and stuff holes with half of the crushed garlic.
Combine the remaining garlic, jerk seasoning, and salt, rub all over pork (you may want to wear gloves).
Place in a large container, pour the lime and orange juice over the pork; cover and refrigerate 5 hours or overnight, turning pork occasionally so the marinade covers all of pork.
The next morning, put everything in the crock pot and cook on LOW for 9 hours.
After 9 hours, remove pork and shred using two forks.
Remove liquid from crock pot and reserve.
Add shredded pork back to the slow cooker.
Add about 1 cup of the liquid back into the crock pot and taste for salt and pepper.
Let it cook an additional 15 minutes.
Meanwhile make the Caribbean salsa: combine all the ingredients in a bowl, season to taste with salt and pepper. Refrigerate salsa until ready to serve.