Pour sesame oil into a 10- to 12-inch ovenproof frying pan over medium heat. When hot, add mango and stir often just until heated through, 1 1/2 to 2 minutes. Scrape into a blender and add vinegar; whirl until very smooth, then whirl in enough white wine or water to give mixture a very thin, pourable consistency (about 1/4 cup). Pour sauce into a small, microwave-safe pitcher. Wipe pan clean.
In a 3- to 4-quart pan, combine 2 cups water and the tea bags; bring to a boil over high heat. Remove tea bags and add rice and 1/2 teaspoon salt; stir, cover, and bring to a simmer. Reduce heat and simmer, covered, until rice is tender to bite, 45 to 55 minutes (about 20 minutes for jasmine rice).
Meanwhile, in a small bowl, mix 2 1/2 tablespoons water, wasabi powder, and honey until blended. Rinse and dry salmon.
Pour olive oil into the 10- to 12-inch ovenproof frying pan over medium-high heat. When hot, lay salmon pieces in pan, skinned side down; cook, turning once with a wide spatula, until lightly browned on both sides, 3 to 4 minutes total. Remove pan from heat and brush wasabi-honey mixture over tops of salmon pieces, using it all.
Transfer pan with salmon to a 350° regular or convection oven. Bake just until fish is opaque but still moist-looking in center of thickest part (cut to test), 7 to 10 minutes.
Heat mango sauce in a microwave oven at full power (100%), stirring occasionally, about 2 minutes total. Transfer a piece of salmon to each of four warmed plates; spoon rice equally alongside (or set salmon on rice). Drizzle mango purée around salmon and rice. Garnish with chopped cilantro, if desired, and add more salt to taste.