I picked up the car a little while ago. I had the tire shop remount and road force balance the tires on the right wheels and put them on in the right positions. They too thought it was odd that the previous installer did this. I had them do an alignment today also. Car rode smooth as silk on the highway drive home. Lesson learned: When having tires or wheels changed on a car like this, you have to give the installer very specific instructions - and if some other owner or dealer put them on before you were involved, check their work. If they aren't familiar with the car, they may have no idea what they are doing.

 

First off, brand names mean nothing as there are cheap, crappy Potenzas, and there are nice and expensive Potenzas.

As for the vibrating, it could be one of many things including everything mentioned, or it can even be something as simple as a directional tire not pointing toward the correct direction. This might be the case if you moved a wheel from the right to the left.

IMO, just take it to a shop, let them fix it and learn what basics you can absorb from them so you know what to look for next time.

This is a problem with a very simple solution that shouldn't be expensive to fix, and with the limited amount of information you are able to gather and convey to us so we can give you a definitive answer, we're just going to confuse you with too much information here.