Ichigo may seem like a one off outlier, but in fact, there was another character, mentioned by Nimaiya himself, who was not a Gotei member but had a zanpaktou, Zaraki. Kenpachi Zaraki took an Asuchi off of a dead shinigami, who he may or may not have killed first. This gave him a zankakuto that he used to great success against the Kenpachi of that time. This shows Asuchi are transferable to some degree.
Second and also the important, when Ichigo first got his powers, he got them from Rukia. Rukia was an above average Shinigami who already had shikai. When she gave him his powers, she did not find it strange he had a Zanpakuto, she rather found that its massive size was strange. She, someone who had to get an Asuchi to have a Zanpakuto, was not focused on Ichigo's possession of one, Which hints that she gave him hers.
So, Ichigo most likely got his Asuchi from Rukia, But that leaves a few plot holes in place. When did she get it back, or did she ever. If she never got it back, why did Nimaiya say he did not have one, and why did Rukia clearly have one during the Arancar arc?
This all boils down to being a Plot hole. Asuchi were not fully fleshed out in the beginning of the series, so they were mostly left vague. But that is not the question here, The question is why they were not surprised he had one. The best answer for that is unfortunately only Theory, the theory that they thought he still had Rukia's Asuchi, or perhaps obtained one from someone else somehow. As noted with Zaraki, it is entirely possible for non Gotei 13 members to obtain Asuchi, though it is rare. In any case, it did not matter to them. If they thought about it, they would have probably thought he stole/borrowed it from Rukia, or maybe though some unknown means obtained a second one.
So, Basically, when he showed up, he had a Zanpakuto, how he got it was irrelevant to them. Though very rare, there was other methods to getting an Asuchi besides becoming a Gotei 13 Shinigami. From a Plot persepctive, Its a hole. One can only Theorize how everything played out. My personal theory on this is that Byakuya broke it, and since he lost Rukias powers at that time, it never healed and was discarded. Rukia then likely got a new one from the Gotei 13.