Pat the chicken dry. Rub with olive oil, then coat all over with taco seasoning, pressing it in.
Preheat the air fryer to 370°F (188°C). Cook the chicken in a single layer for 10 to 12 minutes, flipping halfway, until the internal temperature reaches 165°F (74°C).
Rest 5 minutes, then shred with two forks.
In a small saucepan over low heat, stir the American cheese and evaporated milk constantly until completely smooth, 3 to 4 minutes. Do not boil. Stir in the green chiles and cumin.
Add the shredded chicken to about three-quarters of the queso and stir to coat. Reserve the rest.
Wrap the tortillas loosely in foil and warm in the air fryer at 350°F (177°C) for 1 to 2 minutes.
Divide the queso chicken among the tortillas. Drizzle with reserved queso, top with red onion and cilantro, and serve with lime wedges.