auto belt tensioner

I'd still replace the tensioner. The pulley itself may be fine but not the spring tensioner, so it could be letting slack into the serpentine belt when it's running.

sounds like a UK car :), when was the tensioner replaced, it really should be replaced as and when the belts are, remove the belt and check for side to side movement. although you said it spins smoothly does not mean the bearings aren't worn out, a local garage may be able to sort this for around £50