You're calling me, Julide! No wonder I am all awake now! (it's almost 4 am over here!)
I have not heard of a "selling supervisor" before but just "supervisor". I have a lovely one at my store.
They are supposed to have the best product knowledge on skins, colours, wearability, history of hermes and of course selling techniques. They also guide the SAs so that there are no squabbles over bag allotment to clients. The one at mine is so super. She's like a little mother hen to all the SAs. I adore her alot.
The next rank up from Supervisors, is Asst Managers. Then Managers, Then Directors.