I do exactly the same and it’s never been claimed as insufficient.
Did you have a term period on your AST contract?
If yes the tenant is liable up to the end of the fixed term, irrespective of whether they lived there or not.
If not the council will only make the tenant liable if he lives there, and does not have any C. Tax liability on any other property, as they argue a resident can only pay for one property at a time.
That’s only true if there is a clause in the contract making the tenant liable for the Council Tax.