If you thought they would happen at night, why would you willfully let Town go into a Night where they don't have any concrete idea that Cult exists, on the off chance that you might get targeted by the recruiter? How does that make sense to you.
And another thing I've been holding onto. If we're looking at flavour, why would Eula have an immunity from joining the Abyss Order? She has no relation or relevance to Lumine or the Abyss. What possible reason could there be that Kaeya, Diluc etc could join the Abyss, but Eula cannot? This game has clearly made an attempt to be related to flavour, so what's the flavour justification here? They just... stopped following flavour when they made your role?