The nerve!!

He's angry at the mc for getting fooled by the younger celebrity guy. The real question would be, does he have a right to be angry at the "unequal treatment"? Well, if we talk from the emotional side, it's definitely a "no," but it's different if we're talking about his duties as a professional manager: from that perspective, the ML at least right in one thing, that mc works for him now, he's the one paying the mc's salary now, so the mc has no business wasting time with another celebrity, anymore. The mc accepted the ML's offer knowing it's a full time, exclusive job, but many times he ditched the celeb he was getting paid to take care of (and to accompany to events) in order to go see what the younger guy wanted. It's obvious that, if this kept on, it would end up causing him to really start neglecting his current job.

When he said that, he was talking about their relationship, like him and Yeongwoon fooling around but the latter drawing an invisible line all of a sudden, declining his kiss even though he said that he'd "take care" of him.
I agree on your last point, Yeongwoon has a duty as the manager and I understand that he's angry at him for getting fooled by the younger celebrity but that's only talking about the perspective of a celebrity not wanting his managers attention being elsewhere and that isn't what he meant while saying that imo. It was purely an emotional response, I don't think the ML felt that the MC neglected his duties or would do do but instead got upset that he can't manipulate him as easily as in the past. Then again we don't know their full backstory yet ╮(￣▽￣)╭ I'll give their relationship a chance but the ML personality is still iffy.