In book 4 in the Pensieve chapter Dumbledore says it before Voldemort's downfall that Snape came to their side. I'm guessing that there was a bit of time between him overhearing the prophecy in the Hog's Head and James and Lily dying. In that time Voldemort must have interpreted the prophecy as being about Harry, Snape heard about the interpretation and decided to become a spy.