Mix soy sauce, brown sugar, garlic, turmeric, cumin, and lime juice in a bowl. Add the chicken pieces and toss ensuring they're well coated. Marinate in the refrigerator for at least 1 hour or overnight.
Preheat your air fryer to 360°F (182°C). Thread the marinated chicken strips onto the bamboo skewers that have been cut to fit your air fryer.
Place the skewers in the air fryer basket in a single layer. Cook for 4-5 minutes, then flip and cook for another 4-5 minutes, or until the chicken is cooked through and slightly crispy on the edges.
In a saucepan over medium heat, whisk together peanut butter, water, soy sauce, lime juice, brown sugar, chili paste, and garlic until smooth. Add more water if needed to reach your desired consistency.
Once cooked, place the chicken satay on a platter. Serve with the warm peanut sauce either drizzled over the skewers or on the side for dipping.
Sprinkle with chopped cilantro and accompany with lime wedges.