Well is your subscription of avast running out ?
The legit pop-up starts about 21 days before the expiry date, see image.
My assumption is that these checks are carried out when you try to update.
Is this the Home or Pro version of avast ?
Without seeing it, the guy at your computer store is speculating and up to a point so am I as I can't see it either.
So a screen shot of first the alert (if different to Scott's) and then the expanded window would be more helpful.