>How does the spent fuel get aerosolized and into the atmosphere?

I'm not an expert, but fuel reprocessing is generally done is an aqueous state. The widely used PUREX process, for example, starts with dissolving the spent fuel in nitric acid. Splashing or boiling the liquids involved will cause the formation of aerosols. In particular, concentrated nitric acid tends to react with things quite vigorously, generating a lot of heat. The process also uses flammable liquids like kerosene and hydrazine.

Some radioisotopes also have compounds that are volatile. Ruthenium, in particular can form Ruthenium Tetroxide which boils at only 40C.