In. Well at least I can understand these rules. But am I right in understanding that there's no night phase here?
Correct enough.
What happens is the Purifiers and Threxes send in thier PMs during the day phase. At the end of the day phase, I send the game into twilight, which you can call a night phase. During twilight, I figure out everything that would have happened if we had a proper night phase, then we move into the day phase.
(And Crockett, I believe it's worded fine - Instant Night sums up the gist very well.
If you want to suggest a better wording, feel free.
As for the mafia, they send thier PM in advance on the day phase, just like Purifiers. I wouldn't call that badly worded, because of this quote:
Every Day, the Threxes may appease one person to Espithel.
I'll spruce it up a bit, though.)
When the lore gets put up, thematically it's because you're in a giant opaque dome, meaning you can't tell whether it's day or night. Hurray for lore.