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.
Meanwhile, make the salsa by stirring the mango, lime juice, orange juice, chilli, red onion, red pepper, green pepper, parsley and black pepper together in a bowl. Refrigerate for 1 hour to allow the flavours to blend.
Preheat barbecue for medium-high heat and lightly oil the cooking grate.
Remove the tilapia from the marinade, shaking off any excess. Wrap each fillet in a piece of foil.
Cook the tilapia on the preheated barbecue until the flesh easily with a fork, 3 to 4 minutes per side. Spoon the salsa over the tilapia to serve.