The most thorough investigation of this dish seen is on Serious Eats. But, basically, a salsa is made with chipotle peppers and a little adobo and the chicken is slow cooked until it shreds easily. Including tomatillos and fish sauce? Maybe not. In a pinch, Kirkland Salsa is used for the "salsa" and chipotle powder, oregano, garlic powder, cumin and salt added to the sauted onions and whatever else is included.
Chicken has a hard time standing up to corn tortillas. Recipes usually pair with flour tortillas, a much friendlier environment for chicken. But the tinga recipes work fairly well in the corn tortillas.