There's a difference between apologizing because you want something from someone, and apologizing because you're genuinely sorry.
This man apologized to Mayu's mother, didn't try to convince her to forgive him, agreed to never come back, and even held his promise not to approach Mayu. The two past encounters were purely coincidental. Him clearly ignoring Mayu (until she approached him of her own accord and tried talking to him) is evidence of that.
He seems like the genuinely sorry type to me.
That doesn't excuse what he did, and I agree that apologizing is no proof he's changed.
However, he's doing all the right steps towards redemption, and I think he deserves some slack.
That doesn't mean he should be forgiven, but repeatedly saying he deserves a beating is just childish at this point.
The man's learned his lesson and moved on. You should too.