Make the sauce: whisk together everything except the water until smooth, then add the warm water a splash at a time until it is pourable but still coats a spoon.
Split the sauce: set aside 1/3 for dipping and the cucumber side, keeping it away from the raw chicken. Use the other 2/3 to marinate the chicken.
Add the thighs to the larger portion of sauce, turn to coat, and marinate at least 1 hour, ideally 4 hours or more, in the fridge.
Shake the excess marinade off each thigh so the sugar does not scorch. Air fry at 390F for 10 minutes.
Flip and air fry another 8 minutes, until the internal temperature reaches 175F.
Loosen the reserved dipping sauce with a splash of warm water if it thickened. Serve the chicken over rice with the dipping sauce.
Optional: toss thinly sliced cucumbers with a spoonful of the reserved sauce for a cool, crunchy side.