Brother Hope takes a deep breath and centers himself. He runs through a few of his favorite litanies and prays, quietly, for guidance.
Is he psychotic? He's certainly believing things that don't seem to reflect consensus reality. But from the evidence he has, that this man breaks the laws of physics-- no, doesn't break, that's blasphemy, the logos never changes, it is the same across all of space and all of time, only our knowledge of it changes-- that this man breaks the best current models of how physics works is simply the most accurate hypothesis. Other people responded the way he'd expect them to respond, if this was true. Sister Kutka took over the hostage-taker and left him to handle the unforeseen event, as they'd trained. They had not encouraged him to go speak to his spiritual director.
He could be doing a more complex hallucination of all of his experiences. But this kind of all-encompassing delusion is not known to happen to psychotic people; it could be dream-logic, but if that's the case everything he's experiencing is wrong. That kind of utter skepticism is a known red flag which everyone in the Teachingsphere has been trained to avoid. Unless you have specific reason not to, you trust the evidence of your eyes and ears about what's happening around you. To do otherwise makes delusion even more likely.
He centers himself again. So there is a member of a nonhuman sapient species who can do things previously believed impossible, and Brother Hope is making first contact. Brother Hope is good at his job, but part of that is that is that he doesn't have any delusions about how good he is at his job; he's the best peaceful-resolver-of-stressful-situations in the city, but he's not nearly good enough at it to work at a prison-monastery, and it's far from obvious that this is the appropriate skillset for this job anyway.
Of course, it's far from obvious that it isn't, especially on short notice.
Brother Hope prays for patience, slowness to anger and quickness to forgive; he prays for the ability to step outside himself and to understand the ways that the aliens may be different; he prays for kindness and compassion; he prays for the ability to notice whether his skills are the ones needed, and get in someone else if they're needed, without desire for fame or to push off a terrifying responsibility on someone else; he prays for any skills he might need he is not wise enough to ask for. He reminds himself of his favorite sages and imagines their response to this situation. Finally, he prays: thy will be done.