Hello, and sorry for a late response. I was on a vacation for two weeks so only now catching up with things.
I tested on several families.
Case 1) A family of five sims, created at the game's launch, very old household. No new additions, additions have nothing to do with it. They have completed most of the collections in the game in their long playtime. Some of the collectibles are probably set on display in the house, some in the storage box in the lot, it's possible some were in inventory too, not sure. I cannot guarantee they even have all the collectibles in their possession anymore.
I went to Manage Households window and removed two of the sims into their separate household. Then I loaded back to the original household that still had three sims left. All their collections were reset to zero. I did not look at the Aspirations at all, so don't know about that. Talking only about the Collections, not Aspirations.
Removing just one sim did not reset the Collections, it needs two sims removal.
Case 2) This is when I hadn't yet realized what was going on, so that's why there's the additions juggling. A couple with a teenage daughter. Removing just the teenager daughter into her own household did not reset the collections for the couple. Adding two random townies into their household and then removing them again did. I don't think adding sims at all matters, that's just what I did when I hadn't yet figured out what was going on.
It's better to focus on Case 1 since there's no adding whatsoever, which makes it clearer. So: removing one sim in Manage Household does not reset original household's collections. Removing two sims in Manage Household does. Yes, the original household that had the Collections done, still living in the same lot they were in when they completed the collections. I did not even check the collection situation of the sims that moved away, I know they should be reset and that's fine.
No traveling was needed for the reset to happen.