Yes, the adult can be charged with assault, since any unconsented or unwanted contact, including a push, can be assault. If charged, the adult could raise self-defense as a defense to the charge: could claim and try to show he/she was attacked first and only pushed to defend him/herself. Self-defense though, is a *defense*--that is, it is something you raise after being charged; it does not necessarily prevent you from being charged in the first place, though in a situation like the one you describe, the prosecutor may choose to not bring charges.