My impression of the Matachin Tower is that it is not a "one day" service place, like a dry cleaner's shop. To the contrary, clients wait months, seasons, even years before being physically "processed" (the wait itself being a form of psychological "processing").
So Cathy the naughty monial is arrested on whatever trumped-up charges or official pretext for disappeared persons (that is, why should the city/state/government even give a fig about her; let alone put her in the maximum security prison--aye, there's a big hairy mystery).
We understand from Ouen that she and he trysted for a while before she was disappeared. If we are to believe that Severian is a product of that union, then nine months or three seasons later, Severian (and twin sister) are born.
Why hire a wetnurse when you've got this woman lactating for free? Who knows, it could be done--depends upon the application; the larger point that the assayist may be trying for.
And so on.
Born in a locked tower, to a fallen professional virgin who is probably of exultant stock, of a mysterious union with an almost unknown father (no jokes about "showers of gold," please).
=mantis=