The time to deal w/ a bully is the moment the bullying starts and to do so in a quiet, non-agressive but totally firm and implacable way while - assuming it is safe to do so - exiting the situation. Sometimes to avoid pointless arguement/escalation, it actually becomes necessary to stay so on message verbally that it begins to sound silly - like a mantra. I've never had this not work even when I have in fact felt I might be in actual danger.
I like this answer.
Staying and letting him beat you up is potentially dangerous for you, and makes you complicit in the lesson he is giving his students. As you observed, it's not an Alpha Dog response, no matter what you do after class.
Staying and reversing his technique (during class) might work in some situations, but is risky because it might just make him angry, and then someone (probably you) would get hurt. As long as he defines the nature of your attack, he will always have the advantage.
Handling the situation as you did still makes you complicit in the in-class lesson to his students, while also putting you on the same level: of taking unfair advantage of a rigged situation. (Judging from the response of those who were there, it didn't establish your Alpha-ness, either.)
Women don't do the Alpha Dog thing in the same way that men do, and I notice that most of the critics of your response are women. I have observed, though, that one way in which Alpha Dogs settle things between themselves is to step outside. If you really must show him "who's boss," then invite him to spar with you, as equals. Since most bullies are also cowards, the chances of him declining the invitation are good, and if he does your Alphaness is confirmed.
"I won't fight with you on your own mat. I'm leaving now."
"If you'd like to spar, we can do that, but I didn't come here to be bullied. I'm leaving now."
(Naturally, offering to spar with him is risky unless you believe yourself to be his peer, which wasn't clear from your post. If you think he's better than you, then it's best to just get out of there.)