Ehhhh not really cause he was releasing the omega pheromones prior to them doing it so no, being injected with huge amounts of semen doesn’t apply for the cause since he was already slowly turning into an omega.
It’s more likely, if it wasn’t a side effect of the drug, then it’s very likely the ML being around the MC so much was what caused it or at least started it. You know, with the whole pheromones at him without realizing he was doing so.

Wait I don't get chapter 2 it says GENERALLY, BITCHING OCCURS WHEN EITHER OF TWO CONDITIONS IS MET:
AN ALPHA IN RUT BITES
THE SCRUFF OF THE SUBJECT'S NECK, OR THE SUBJECT TAKES A LARGE AMOUNT OF SEMEN INTO HIS BODY.SINCE
REI DOESN'T
MEET EITHER OF THOSE CONDITIONS, IT'S NATURAL TO THINK THIS MIGHT BE A SIDE EFFECT OF THE DRUG...
But he did meet one of the conditions he had a large amount of semen in him and sigma is alpha pheromones and cum so? They said sigma is a superior alpha so even more like