The chances are that the rear tyres have worn on the inside edges in a "saw tooth" pattern. This is caused by misaligned suspension geometry. More often that not, too much rear toe in. When it gets really bad, it will make a droning noise, much like a worn wheel bearing and send vibrations through the whole of the car. As the wheels have been refurbed, the chances are it's had a few too many hard comings together with the kerb which could knock things out of shape
Run your hand over the inside tread of the tyre from front to back and you'll feel if there is irregular wear.
Unfortunately the only cure for this is new tyres and then have the suspension geometry checked and adjusted accordingly. Bridgestone and Dunlop tyres are the worst for suffering this type of wear, so it would be advisable to fit another brand.