I'd lean towards a bug. There's other things that complete if you are in one or more clubs (like if you buy perks for one club, they are available in the other).
Just one question: Was the leader of that 8 Sim Club in your household or in a different household ?
The leader who had the 8 Sims goal completed was in my household. Rebecca is part of my household who is the leader of the Goths Club, Rebecca is also a Member of the Art Lovers Club that Zoey (also part of my Household) started. Below shows my Household and Club information.
Miller-Couture Household
Goths' Club Members
Art Lovers' Club Members.
Zoey and all other members of the Miller-Couture Household.
So there could be two scenarios that trigger the issue (both faulty of course)
It was triggered, because another Sim in your household fulfilled the criteria or it was triggered because the Sim with the aspiration was in two clubs as you suggested above.
So I guess the next test would be to have the same scenario but move the Sim that's the leader of the other club out of your household.
I have removed the other Club Leader (Zoey) from the my Household and had Rebecca start a Club while part of the Art Lovers Club and the goal also completed. I also tried the Pancakes Household with Eliza by having her join Art Lovers and then starting a Club, she also got the Goal as well. It appears that even leaders with 8 Sim Clubs part of different households will still complete the Lead a Club with 8 Sims goal.
I used testingcheats true and aspirations.complete_current_milestone to get to the Leader of the Pack milestone for the test which was used on Urblake, Rebecca, Zoey, and Eliza from the Pancakes household. I started Art Lovers with 6 Sims and set the Club Activity to Paint to allow me to get 750 Club Points to get both Capacity upgrades. To prevent the Welcome Wagon from appearing during test, I edited the Municipal Muses lot in Willow Creek to include a basement and easels and did the Gathering on that lot.
I could guess why none of the default Clubs have 8 Sims because belonging to one the Clubs while being a Leader of another Club would allow the Goal to complete instantly upon reaching the 4th Milestone.
