Heat oil in a large non-stick skillet over medium-high heat until oil begins to smoke. Place salmon, flesh-side down, in the hot skillet and cook until edges are just starting to cook through, about 2 minutes. Flip fillets, remove skillet from heat, and let fillets sit in the hot pan until cooked through, 2 to 3 minutes more. Transfer to a plate and top with chilled mango relish.
