Peel and section oranges over a bowl; squeeze membranes to extract juice. Place orange sections and 1/4 cup juice in a medium bowl; reserve remaining juice for another use. Discard membranes. Break orange sections into small pieces with 2 forks. Add papaya, cilantro, jalapeño, onion, 1/4 teaspoon cumin, and 1/4 teaspoon salt; toss gently, and set aside.
Place almonds in a shallow dish. Sprinkle turkey cutlets with remaining 3/4 teaspoon cumin, remaining 1/2 teaspoon salt, and black pepper. Press both sides of each cutlet into the almonds to coat.
Heat oil in a large nonstick skillet coated with cooking spray over medium-low heat. Add cutlets, and cook 6 minutes on each side or until turkey is done. Serve with salsa.