Pat dry the salmon filets with a kitchen towel or paper towels and set them aside.
Heat a skillet over medium flame and add water, brown sugar, soy sauce, rice vinegar, garlic, and ginger. Bring the sauce to a boil.
In a separate bowl, prepare the cornstarch slurry by combining cornstarch and water. Add the slurry to the sauce and continue boiling until the mixture thickens. Simmer for 3-4 minutes. Allow the teriyaki sauce to cool down.
Place the salmon filets in a bowl and pour half of the prepared teriyaki sauce over them. Marinate the salmon for at least 30 minutes.
Meanwhile, prepare the mango salsa by combining chopped mango, red bell pepper, red onion, jalapenos, cilantro, lime juice, and salt in a separate bowl. Mix well and set it aside.
Preheat a griddle or grill to medium heat. Place the marinated salmon on the griddle or grill and cook for 4-6 minutes on each side, or until the salmon is cooked through. Baste a couple of time through out the cooking process.
Once done, brush the reserved teriyaki sauce over the salmon and garnish it with green onions and sesame seeds. Top the salmon with the prepared mango salsa.
Serve the grilled teriyaki salmon over rice, with lime wedges on the side.