I'm sorry to say but I've had bad experiences with almost all of the blue area tire shops. They are the worst of the worst. Most of their tires come smuggled because I've seen them getting unloaded and they charge an insane amount for the balancing/alignment in comparison to other good shops. It's the whole lot of them, especially the few that are in that one block
The the vibration is shifting when the wheels were shifted, thats a clear indication the issue is with the tires. Either rebalance the front tires by another shop and ask them to inspect the tires. If the wheel is bent, they might point that out too but it's rare for a damaged wheel unless you hit some major potholes or went offroad. Plus, a bent wheel would have shown signs with the older tires too.
Regardless, see what the other shop says. BTW, check the MFD on the new tires, all 4 of them