In a small bowl, mix tamarind pulp and 3/4 cup boiling water. Let stand until lukewarm, 8 to 10 minutes; rub pulp with your fingers to mix well and release from seeds. Rub mixture through a strainer into a 10- to 12-inch frying pan; discard residue.
Add sugar, vinegar, soy sauce, and hot sauce to frying pan. Bring mixture to a boil over high heat and stir often until reduced to about 3/4 cup, about 5 minutes. Scrape the reduced sauce back into a bowl (or, if making up to 1 week ahead, into a jar or refrigerator container; cover and chill).
Rinse the frying pan and wipe dry. Place over high heat and add the oil; when hot, add shrimp and stir until they begin to turn pink, about 2 minutes. Pour into a bowl. Add the tamarind sauce to pan and stir until it's boiling vigorously; return shrimp to pan and stir until opaque but still moist-looking in center of thickest part (cut to test), 3 to 6 minutes longer.
Spoon shrimp and sauce onto plates or into a bowl. Garnish with green onions.