The one thing that's getting me is, if the entire thing is play-acting (as it seems to be) Why keep the Jaegers in the dark?
Like, turning the Castle off makes sense so the Heterodyne can't cheat, but the Jaegers are explicitly perfectly free-willed.
"You all go drink, I'm going to go get chased around by the townsfolk all night"
"Hokay Boss! Haff Fun!"
And then they just, don't intervene, because they know the Heterodyne is in no real danger, so the Heterodyne can't call upon them to help cheat.
Which of course raises the question of how old this "Ritual" really is? The Jaegers are, presumably, recruited from the Mechanisburg population, all of which seems to at least be AWARE of the tradition (Giant mobs through the streets are hard not to notice), and seem to undergo the process AFTER reaching Adulthood.
So, unless the Heterodyne Hunt postdates the youngest Jaegers, at least some of them MUST know what's going on out there.
Which is of course assumes that the Jaegers Don't Know. We only have Oggie's word that the Jaegers are completely in the dark about what the Heterodyne gets up to after they reach the Jaegerhall after all.
If the entire thing is a citywide LARP of the Heterodyne getting chased by angry mobs, maybe part of the pageantry is that the Jaegers are unavailable, since even if they didn't intervene, they might lurk around watching things, which would ruin immersion.
So the Jaegers get a big party so they don't feel bad about missing out on the fun, and all pretend like they have no idea what's going on outside, making jokes like "Wow, I hope the Heterodyne is having a good walk home, and not trying to take the alleyway off Skull Street" "Yeah, I saw a bunch of people putting a bunch of furniture there" "Wow! That's dangerous! If somebody, say, the Heterodyne, were to try to flee down that alley they would be trapped by barricades!"
Edit:
Heck, for all we know the Chase is being projected into the Jaegerhall by some version of the Library Map, and the centerpiece of the Party is the Jaegers watching the Heterodyne get chased around by the townsfolk.
Oggie could have been trying to surprise the Professora.