It varies, it could happen tomorrow or the day after or it could be late July for all anyone knows.
Don't forget that theres hundreds of emails they need to send, and on top of that they need to make sure theres space for the people they cast to come in for paperwork, so its gonna take a while. My advice would be to keep an eye on whatever range you were told the paperwork dates should be, and thats likely the range when a majority of casting emails will go out, but even then sometimes it takes longer than that. A few years back I didn't get an offer until 2 weeks before the event started lol.
Regardless, even if you don't get cast, it looks like house host positions are still available if you still want to be a part of the event outside of just scareacting, which is still fun.