No one wants to walk around with red, swollen skin around their eyes. This is exactly what can happen after a wax on someone even if intensive exfoliating skincare products aren't being used. (See more waxing precautions.)
It can simply be a side effect, which can last for a couple hours, on those who have very sensitive skin. How can this be prevented? The quality of the wax and the technician definitely has a bearing on the results. But switching to another similar method is an option if it's a recurring problem.
Take sugaring for example, it still pulls hair out from the root like waxing, but the ingredients are different. Wax is generally made up of resins, and sugaring contains natural ingredients like sugar, lemon juice, honey, salt and water.
Sugaring is known to stick less to skin, therefore be less painful. It's also considered less exfoliating than waxing, which is way it can be re-applied to the same area of skin to get missed hair.