I don't think the seme was nearly so worried about the secret as the uke was. But even then the seme mentioned at one point he believed uke was an alpha. He saw the ID card and trusted that he didn't lie to him. The way it's written implies that the secret itself is the fact that the uke has a uterus. His gender does not seem to be a point of debate amongst the two of them. But common sense should have told the seme that the uke had a uterus (or that there was something different about him physically) when he showed up with a child. Especially if seme did not have any doubts about uke's gender after that, which he didn't seem to. Then common sense should have kicked in (or, at the very least, a basic understanding of science).
Well it could also be common sense that he was an alpha who turned omega. Because at one point semem did say your in heat but where's your pheromones which (to me) implied that he thought he was an omega. I think this would be more easier or mornalong the lines of common sense than oh he's an alpha with a uterus.
I've heard that expression applied for alphas as well in other omegaverse stories "in heat" as opposed to "in rut" and am willing to chalk that up with either the way the story is written or translated, without there being any further intent. The pheromone thing however, I agree with also should have been another indication that there was something unusual about his body. But I once again think that the uke is the one who put way more stress on himself about "the secret" than the seme did.
I don't know if I am missing something but the first volume made no sense to me. His big secret is that he has a uterus even though he's an alpha, but he had already told the seme that he was an alpha (PROVED it with an ID card) and then later showed up with a baby. So unless the uke kidnapped seme's child by another person, or the baby was brought by a stork then common sense is going to already inform him that there is a uterus involved somehow.