"after-fire" means "after" the combustion chamber. It happens in the exhaust, not out in the open air. Whether or not it can hurt anything depends on the system. Some airplanes have mufflers that are nothing more than a thin walled can, some have internal baffles and some airplanes have no muffler at all. With straight pipes you will only get mild individual pops and virtually no chance of any damage but with a canister muffler such as the Hanlon-Wilson and various other types used on a variety of GA aircraft the volatile mixture can accumulate and result in a significant explosion that absolutely can cause damage.