Place the pineapple, onion, bell pepper, jalapeno, lime zest, lime juice, and cilantro in the bowl of a food processor fitted with a metal blade. Pulse until the ingredients are chopped coarsely, leave plenty of texture.
Transfer to a medium bowl and stir in the preserves and season with salt. Serve either a t room temperature or lightly chilled.
Preheat the oven to 425°F Line a rimmed baking sheet with aluminum foil.
Trim away any loose fat or silver skin from the tenderloins. Pat dry with paper towels. Combine the brown sugar, cumin, chili powder, paprika, salt, and pepper in a small bowl. Rub the mixture over the pork and shake off any excess. Turn under the small ends of the pork to make the thickness of the tenderloins fairly uniform.
Roast the pork until it reaches an internal temperature of 150 F, about 20-25 minutes.
Transfer the meat to a cutting board and let rest for 5-10 minutes before slicing. Slice the meat and serve with the salsa.