No, why are you all still getting that wrong, it's written in that story.
The dog trauma began earlier. Why do you think Chase got that trauma, only because Grayson was telling him? No, there was a dog present during his first rut, because Grayson panicked and didn't know what to do with Chase, who was in a bad condition back then. Nothing happened, and Chase doesn't really remember, but knew that there was a dog present. But that was much earlier, when Chase still lived at their family home, having his first rut.
That + Grayson planting doubts to make him release pheromones, are the origin of the dog trauma. It had nothing to do with the first night with Josh.
Chase knew he slept with a human that first night with Josh, he searched for that person and couldn't find him. And with time he got doubts etc., started doubting himself, even thinking of a dog. Josh was the only one who knew what happened, that Chase slept with someone that night.
And for accepting that child so easily, he wanted for Josh to stay with him no matter what's the cost. And now they have a child, which will bind Josh to him forever. So no wonder he is happy.

He may be an actor, but that "oh nice, I have a five year old child I didn't know about with someone I marked unknowingly on the same night my fear of dogs trauma began because no one told me sh!t" is not very Oscar worthy