Start by rinsing the jasmine rice under cold water until the water runs clear. This removes excess starch and prevents the rice from becoming sticky. In a saucepan, combine rice, coconut milk, water, sugar, and salt. Bring to a gentle boil, then reduce heat, cover, and let it simmer until tender.
In a mixing bowl, combine diced mango, avocado, red onion, and cilantro. Add fresh lime juice and a pinch of salt. Gently toss everything together, being careful not to mash the avocado. Let it sit for a few minutes so the flavors blend beautifully.
In a small bowl, whisk together lime juice, olive oil, garlic, salt, and pepper. Brush or drizzle this mixture over the salmon fillets evenly. Let the salmon rest for about 10–15 minutes so it absorbs the citrusy flavor.
Preheat your grill or grill pan over medium-high heat and lightly oil the surface. Place the salmon fillets skin-side down and cook for about 4–5 minutes per side. The salmon should flake easily with a fork when done.
Fluff the coconut rice with a fork and place it on serving plates. Top with grilled salmon and generously spoon the avocado-mango salsa over each fillet. Serve immediately while everything is fresh and warm.