Josh had a crush on Chase and had an oops baby with him but knew that realistically it was not possible for them to be together because Chase seemed to be very violent and crazy so he left. When he came back again he had the same impression of Chase but now that he came to know he's just a scared child inside he couldn't deny his feelings anymore and is head over heals in love with Chase.
The novel is where all of their inner thoughts are known, but that's why I said it was a little spoiler since it's Josh himself who tells Chase later on that he was first love in childhood. Sadly, the person who translated the novel took it down recently because a paid platform bought the license, I think.

He took this job taking care of the kid’s dad for the money, okay that’s understandable.
He wants to hide the fact that he is an omega and he has a child with this guy because he was a major jerk, yep totally get that.
Then suddenly he is all over him??? Initiating sex, giving forever pinky promise, offering to kill his enemy (despite having a child who depends on him) yeah that could have been a joke but it didn’t sound like that.
Why exactly he is trying to do here?
I would like to enjoy this one, but that jump in logic and the inconsistency in his behaviours just bug me so much