Responses
First rut (dog was present) and rut he spent with Josh are not the same, somehow most confuse those two ruts.
The reason why they make him think that?
It's Grayson's misguided way of helping Chase. He is not aware how damaging his way of helping can be.
Chase's unwillingness to release pheromones is a serious problem.

Chase didn’t actually spend his rut with a dog. From what I remember, his family manipulated him into believing he did. I’m pretty sure that was actually the first time he spent it with Josh, but I can’t remember the exact reason his family lied about it. Either way, his family is extremely messed up, and he wasn’t treated well growing up.
He absolutely did not have sex with a dog. The idea itself is disgusting and horrible, even more so because Chase was made to think it was true. I think the author included that detail to highlight just how abusive and twisted his family (especially his brother) really is. And yeah, omegaverse elements already echo real-world canine traits, so adding something like that is especially unnerving and uncomfortable to read.