Mites are attracted to moist places and it not uncommon to find them in and around moist soil However, to find that mites surface upon watering suggests that the mites are already in the soil and are surfacing to escape drowning.
After watering the soil you may see some mites there. There is nothing to worry about it. It is very common. It is the symptom of good soil. Most of the mites won't cause any irritation or damage to the plants. But some of them may bite and cause irritation to humans.