CHECK THE TORQUE ON THE LUG NUTS!!! Since the rear wheels were just off, it's HIGHLY possibly they weren't torqued correctly or are simply lose...especially if it's happening at higher speeds. Past that, what Roy said, gotta know where the vibration is being felt to help diagnose.

Was the vibration there before you replaced the rear tires? If not, also possible to have a broken belt inside the tire, which you wouldn't be able to see until the tire exploded. Possible they forgot to balance the rear tires as well. Or, something going wrong with the front tires.

Probably just added more to your list of concerns, but I'd start with what you did recently to the car and work backwards from there. Obviously, if it wasn't there prior to the tire change, then might have something to do with the tire change.

Hope that helps.