A "praeses" is a leader. Archaic meaning of provincial governor, derived from the latin for "he who presides." I suppose if you wanted to be inaccurately direct, you could say it translates to English as "president." But that's not quite it. Anyway, it came to refer to particular class of provincial governor. Basically the bottom rung of three.
In 18th century German, the title designated the equivalent of a PhD advisor/mentor.
In modern terms, it's used as title for "Chairman" in a handful of religious settings and student societies.
Speculation:
1. The Praeses is a machine. While very little is actually impossible--just extremely unlikely is some cases, computers breaking their coded rules is colloquially "impossible." It certainly the kind of thing you expect someone to say of computer, especially in a scifi setting. "TX71 killed Jones? But that would violate the first law! That's impossible!"
2. Alice referse to it with the genderless pronoun "it" rather than "they." In English, that's bad form. No one need assume they are speaking English, but it's a general rule of storytelling clarity that you don't go using words in non-standard ways without some kind of hint that you're going to be doing that.
3. They have transporters in the Outside. I'm hoping against matter/energy conversion, as that gets weird.
4. Alice is the local equivalent of a Praeses, or has been deputized by the same. She's too well informed. The fact that she can't directly, or via appeal to higher authority, send the Vicissitudes home suggests either a lack of ability or a rule that she can't break.
5. The Vicissitude Praeses is a singular entity, or a collective. It is not a "one of many" That's why Gavia calls it "the" and Alice says that Ardent tricked it then Gavia convinced it. Alice appears to be saying that they both interacted with the same one thing.