Serve this dish with in-season fresh fruit for optimum flavor and texture.
Preheat grill to 350° to 400° (medium-high) heat. Stir together 4 tsp. jerk seasoning, 1/4 tsp. salt, and 1/4 tsp. pepper in a small bowl.
Remove silver skin from tenderloin, leaving a thin layer of fat. Brush pork with 2 tsp. olive oil.
Sprinkle 1 tsp. seasoning mixture over pineapple rings. Rub pork with remaining seasoning mixture.
Grill pork and pineapple rings at the same time, covered with grill lid. Grill pork 10 to 12 minutes on each side or until a meat thermometer inserted into thickest portion registers 150° to 155°. Grill pineapple 2 minutes on each side or until grill marks appear. Remove pork from grill, and let stand.
Meanwhile, puree 2 pineapple rings, 1 Tbsp. water, and remaining 6 tsp. olive oil, 3/4 tsp. jerk seasoning, 1/2 tsp. salt, and 1/4 tsp. pepper in a food processor or blender 30 to 60 seconds or until smooth, stopping to scrape down sides as needed.
Combine pineapple mixture and salad greens in a large bowl, tossing to coat. Cut pork into slices. Arrange salad greens, sliced pork, pineapple rings, and mango on a large serving platter. Garnish, if desired.