To make marinade, whisk together olive oil, lemon, parsley, garlic, basil, salt and pepper in a bowl. Pour into large resealable bag and add tilapia fillets. Seal bag tightly and coat fillets. When done coating, open seal on bag, squeeze out excess air, and reseal. Marinate in refrigerator for 1 hour.
In the meantime, while tilapia are marinating, begin making mango salsa. Combine mango, red bell pepper, red onion, cilantro, and jalapeños in a bowl, mix well. Add lemon and lime juice to bowl, toss well to coat other ingredients. Season with salt and pepper to taste and refrigerate until ready to use.
Preheat an outdoor grill for medium-high heat and lightly oil grate with grape seed or safflower oil.
Remove tilapia from marinade bag and shake off excess. Grill fillets for a few minutes on each side.
Remove tilapia fillets from grill. Plate to serve and top with mango salsa.