Stir the olive oil, garlic, basil, black pepper, and salt together in a bowl. Put the tilapia fillets in a resealable plastic bag; pour the olive oil mixture over the fillets and seal the bag. Marinate in refrigerator for 1 hour.
Make the salsa by stirring the mango, lime juice, orange juice, jalapeno pepper, red onion, red bell pepper, green bell pepper, parsley, and black pepper together in a bowl. Refrigerate for 1 hour to allow the flavors to blend.
Preheat an outdoor grill for medium-high heat, and lightly oil the grate.
Remove the tilapia from the marinade, shaking off any excess oil, and wrap each fillet in a piece of aluminum foil.
Cook the tilapia on the preheated grill until the flesh easily with a fork, 3 to 4 minutes per side. Spoon the salsa over the tilapia to serve.