Ideas
I have this problem as well, since 2018.
When I only had one butler (Butler A) active in the save file, the butler stayed put on the household (Household A) he was assigned on. When I made a new household (Household B) and assigned a new butler (Butler B). Butler B stayed on Household B while I was using the same household. But when I used a different household, or when I travel to a different lot, Butler A replaced Butler B in Household B. When I open Household A, Butler A still works there. Both butlers were modified in CAS after they were assigned.
I have experienced this problem since 2018. I distinctly remember because that was the release year of Get Famous EP so I felt that it was fitting to buy the Vintage Glamour pack for the celebrity sims.
I cannot believe that now that I have returned to the game after almost seven (7) years, this problem still has not been fixed. The developers were able to release so many new packs from 2018 up to now, yet they did not bother to fix the existing packs.