According to the text (Anniversary Edition page 90), the unassigned haunts become universal and effect everyone. Which is pretty brutal. I ended up just assigning it to whoever felt appropriate as they entered the room.
One thing I'd suggest from running them is offer people more choices dealing with the haunts. Describe what's going on and ask them what they do.
If they just try to resist or disbelieve the haunt, let that succeed deal them some Wisdom damage (say 1d4 or 1d6, Will save for half). If they stand their ground or give a wishy-washy response, hit them with the written effect. That sort of thing.
The haunts as written aren't very interactive and are basically "Enter the room, creepy thing happens, roll a save. Repeat." Some choices would help people get invested in the growing doom.
That said, the haunts part of that adventure as written was the most scared I'd ever had players. So, if you don't want to do the work rewriting the haunts, just describe things in loving detail and run with it.
Oh, and my favorite from my run through the house: Call for Perception checks. Tell whoever gets the highest that they see something (like a face looking through the window) or hear something (like footsteps on the floor above them, pacing back and forth). If they try to point it out to anyone else, it stops or they simply can't hear it.
So much paranoia.
Cheers!
Kinak