For sauce, in a small bowl combine the first six ingredients (through garlic). Prepare as directed for desired cooker, below.
In a 6-qt. electric or stove-top pressure cooker combine coleslaw mix, shredded carrots, and 1/4 cup water. Place chicken on top of cabbage mixture. Drizzle with 1/4 cup of the sauce. Lock lid in place. Set an electric cooker on high pressure to cook 5 minutes. For a stove top cooker, bring up to pressure over medium-high; reduce heat enough to maintain steady (but not excessive) pressure. Cook 5 minutes. Remove from heat. For both models, let stand to release pressure naturally 15 minutes. Release any remaining pressure. Open lid carefully.
Using a slotted spoon, spoon chicken mixture down center of tortillas (discard cooking liquid). Drizzle with remaining sauce. Top with green onions.