The idea of having to make the sprites happy every single day was so annoying to me I ended up creating a mod where they simply don't give you a Tense moodlet when you ignore them. No more having to appease them all the time. Clingy little buggers. It makes them more like the island spirits. If you make them happy, they reward you. If you ignore them, they just go away doing nothing.
Of course, since I keep telling people that I don't make mods, I just plunked it down in the University chat of Deaderpool's Discord.
As for this bug, I think I know what causes it. Once the first visit triggers, you get stuck in a neverending loop. Sprites leave, which triggers a cooldown, which triggers an event timer, which triggers the visit, which triggers the leaving, which triggers the cooldown... Well, you get the idea. It won't matter if you are a member of the Order or not, once you're in the loop.
I can see why Maxis missed it. It's like chess, they didn't think 5 moves ahead.
I think the cleanest fix is to add a test on one of the timers that checks if you are a member of the Order. If not, timer doesn't trigger and the loop is broken. Going to try that now.
EDIT:
I do believe I fixed it (with help from someone waaaay more experienced) by adding a whitelist-test to the cooldown that checks if you're a member of the Order. If that works, it would break the loop after the next visit and the little critters should stay away. Now to test it.
