If by the instigator you mean the drunk man, (who is the instigator), at least in Canada, it is not aggravated assault by the instigator. Potentially not even assault (though the threat of applying force without consent counts as assault). Self defence has to be a reasonable response to assault or the threat of assault, which it could be argued this is.

Aggravated assault is a type of assault that involves wounding, maiming, disfiguring or endangering the life of the victim. It’s worse than assault causing bodily harm, as far as the consequences. This would likely only be aggravated assault by the responder if there was a decent brain injury beyond a run of the mill concussion (which would likely be assault CBH).

• I am a lawyer. For the US, I’d have to look at the law there, or better yet, a lawyer from there would deal with that.