Preheat an outdoor grill for medium heat and lightly oil the grate. Season salmon fillets with salt.

Cook salmon on the preheated grill until it easily flakes with a fork, 6 to 8 minutes per side.

Combine water, rice wine vinegar, brown sugar, garlic, chili paste, ginger, and soy sauce in a small saucepan over medium heat; bring to a boil. Reduce heat; simmer until barely thickened, about 2 minutes.

Sprinkle basil on top of salmon; spoon glaze over top.