One of your sims must be able to help the VIP, not necessarily the one who needs the badge but one of your sims must qualify otherwise you wouldn't have gotten the task in that room - unless you've demoted one of your professionals or have not yet unlocked the room required
Let's say you have 2 movie studio professionals, A (actor) and D (Director)
If A needs a VIP to complete a badge, D can preform the task and as long as A is active on the shift, A will get credited for the VIP and it will count towards As badge
If A is not on the shift while D preforms the task, it will not count towards the badge
The partially helped VIP or any other partially helped sim will go away to make room for new sims in need of help, it may take a day or a week, I still haven't figured it out but sooner or later the partially sim will go away