I can only guess, but Chase in that commercial was Josh's first love and he is the father of Pete. It was the first time Josh bottomed (Josh saw himself as hetero). And after Chase he never slept with anyone else, before he was a womanzier, even slept with 4 at the same time. He said it was only for Pete that he stopped, but who knows.
And he seems to see Chase in Pete, although he is Josh's mini-me in looks, I mean later he sees what they have in common, but at the beginning of the story... .
So I guess there is something there, some lasting effect, even if it's subcontiously and he isn't aware of it.
If I'm not mistaken, based from the novel, Josh actually likes Chase that's why he slept with him.
And I think with Kieth and Yeonwoo's case, it was explain that the reason why Keith's mark on Yeonwoo disappeared because of amnesia. Yeonwoo basically doesn't have any memory of them having intimate relationship added to the fact that in his memories, Keith doesn't sleep and even hated the idea of being with a male omega. That's why the alpha's mark on Yeonwoo disappeared because in Zig's omegaverse's world, as you mentioned, when it comes to markings, omegas have more advantage than alphas. I hope it make sense.
It has been established many times in this universe that the alpha's marking doesn't matter and that only omega get to mark their alpha and that stays as a permanent bond. So how come Josh still has Chase's mark on his ear? In KML, Keith got marked and he could never bond with anyone else. In KTS, Winston talked about how multiple alphas could mark an omega and ever rewrite a marking but only an omega's mark on an alpha would bond them together forever. It's been bothering me since this story started as to how Josh still has that mark. If the omega doesn't care about the mark, it would fade away. So is Josh willingly keeping that mark? Because I remember when Yeowoon lost his memory, his mark disappeared since he didn't remember Keith after all the drama.