Rinse 1 cup jasmine white rice until the water runs clear. Combine the rice, 1 cup coconut milk, 0.75 cup water, and 0.5 tsp salt in a medium saucepan. Bring to a simmer, cover, reduce heat to low, and cook for 15 minutes. Remove from heat and fluff with a fork.
In a medium bowl, gently toss 1.5 cups diced mango, 1 diced avocado, 0.5 cup diced red bell pepper, 0.25 cup chopped red onion, 0.25 cup chopped cilantro, 1 tbsp lime juice, and a pinch of salt. Set aside to let flavors meld.
Preheat the grill to medium-high heat, approximately 400F. Ensure grates are clean and oiled.
Pat the 4 (6 oz) salmon fillets dry. Rub them evenly with 2 tbsp olive oil, 1 tbsp lime juice, 1 tsp lime zest, 1 tsp salt, and 0.5 tsp black pepper.
Place the seasoned fillets skin-side down on the grill. Cook for 5 to 6 minutes, then carefully flip and cook for an additional 2 to 3 minutes, or until the internal temperature reaches 145F.
Serve the warm grilled fish over a bed of coconut rice and top generously with the prepared avocado and fruit relish.