The redemption arc happened chapters before when he was helping Dan with his sleepwalking that was Jaekyung’s fault and Jaekyung realizing how shitty he treated Dan and trying to make amends with Dan.
Him being a mess over Dan checks for his character because we are shown that how death and abandonment affected his character.
Why he would have a reaction like that to his father who has been extremely abusive towards him mentally and physically? Yes, proving his father wrong was his fuel to become the strongest in his field but that was out of hatred. Plus, you are forgetting that Jaekyung had cried when his mother crushed his dream of reuniting with her after she asked him to stop contacting her because she made a new life for herself without any room for him and that destroy his ability to be vulnerable to others. You forget that part of the reason he falls for Dan is that Dan fully accepts him and will always root for him on his side after Jaekyung bared everything about himself. Dan was the first person who given him the validation that he was looking for that he sought through fighting. The only reason he didn’t pursue Dan because he knew how horrific he has been to Dan but he is willing to be open and vulnerable to Dan again to ask him to stay not because of the jinx but because he loves him. And one that day, Dan gets stabbed.
So it’s really not surprising that beating the shit out of the man who co-conspired the stabbing and hearing that Dan out of the surgery alive but still in critical condition would bring him to tears because for all he knows, Dan can still die succumbing to his injuries so he would sacrifice fighting for Dan to be okay.

the crying seems more from emotional overload/exhaustion than anything, it seems out of character.
see...yall wanted a redemtion arc and got dan stabbed for it lmaoo