Playing off the disc, installed onto the hard drive on 360S.

When I accepted Purity from Vilkas, it went straight to the completed list, and when we fast traveled to the tomb, he walked away. None of the other companions would ask for their part of the quest. -Loaded an old save from before accepting Purity, and after doing 5+ quest for each companion member, none will ask.

Does anyone know a fix for this?

The only fix I know of is to do Farkas' purity quest before Vilkas', which seems to correct the problem. So if you have an earlier save that will be your best bet.