1. Stir together pineapple, papaya, 1 tablespoon lime juice, scallion, 2 tablespoons cilantro, 1/2 teaspoon Cajun seasoning, and cumin in a medium bowl.
2. Combine turkey with onion and remaining lime juice, cilantro, and Cajun seasoning. Form mixture into 3 1/2- x 1-inch patties.
3. Preheat a lightly oiled grill pan over moderate heat, and grill burgers, turning once, 5 minutes per side or until cooked through. (Use a meat thermometer to check that burgers have reached 165°.)
4. Toast rolls on grill. Top buns with burgers and salsa; serve immediately. Leftover salsa may be stored in the refrigerator for up to 3 days. Use leftover salsa with fish, tacos, and tortilla chips.