In a food processor, food prep, blender, or cylindrical container with an immersion blender, process the garlic, onion, jalapenos, lime juice, soy sauce, olive oil, brown sugar, thyme, allspice, pepper, nutmeg, and cinnamon until well-combined and transfer to a slow cooker. Add the pork shoulder and turn to coat. Cook on low 7-10 hours.
Meanwhile, combine the salsa ingredients in a medium bowl. Refrigerate until use.
Once through cooking, remove pork from the slow cooker and shred between two forks. Pour all but about 1 cup of liquid from the slow cooker and return the pork to the slow cooker; gently mix to combine. Serve pork in corn tortillas and top with salsa.