Fumble advance 5yds?

The play I really didnt understand was the botched punt where they called illegal kick. If it was a fumble then an illegal kick, shouldnt it have been the Saints' ball at the spot of the kick and not where it was returned to ? I mean if it wasnt a legal punt, how could it not be a dead ball at the point it was illegally kicked ? Not sure about the rule here, can anyone explain this call to me ?