Trim visible fat and any undesirable parts from chicken breasts and cut each into 3-4 lengthwise strips. Put chicken strips into the Instant Pot with the salsa, onion powder, and garlic powder. Lock the lid, set the Instant Pot to HIGH PRESSURE, 8 minutes.
While the Instant Pot comes to pressure and cooks for 8 minutes, get the green tabasco sauce, fresh lime juice, cubes of cream cheese, and diced green chiles.
When the 8 minutes cooking time has finished, let the Instant Pot NATURAL RELEASE for 10 minutes, then turn the valve to quick release the rest of the pressure.
Remove the chicken strips to a cutting board to cool. Turn the Instant Pot to SAUTE/LOW HEAT and let the liquid simmer until it's cooked down to about 1/2 cup. (This took about 5 minutes.) While the liquid reduces, use two forks to shred chicken apart.
When the liquid has cooked down, turn off the Instant Pot and let it cool for a couple of minutes. Then stir in the Green Tabasco Sauce, lime juice, diced green chiles with juice, and cubes of cream cheese. Whisk the sauce until the cream cheese is all melted and mixed with the liquid to make a creamy sauce.
Add the shredded chicken back into the Instant Pot (you can turn it on low for a couple of minutes if you feel the chicken has cooled down too much) and add the grated cheese, stirring so it mixes with the chicken and melts slightly.
To serve, heat tortillas in a hot, dry pan for about a minute. Fill each tortilla with some of the creamy chicken mixture, more grated cheese, and other toppings as desired such as olives, green onions, salsa, Pico de Gallo, sour cream, avocado, or guacamole.