Hello,
There are a lot of variables here, so I'm going to give this a shit, and I need you to let me know if I'm missing something.
Lowering a car always risks rubbing, I'm sure you know that.
The vehicle should be aligned with the new tires. That will correct alignment, but may make the rubbing better or worse.
If the driver front strut was leaking/failed, that could have an effect on the entire side of the car in a turn, but I would not guess at that without inspection?
The rear spring on the driver side will be more compacted than the rear spring on the passenger side. That's because you sit on the driver side. If having a passenger in the vehicle does not make the passenger rear rub, that might not be the cause.
Check your clearances, find where the tire is contacting the wheel well, and see if that point in the plastic cover sits lower than on the other side of the car.
The reason he recommended the front is because there is more weight in the front, so it can cause a more dramatic shift onto the springs if the strut is not slowing body roll, the reason I don't consider that the problem is because the issue exists when you go over speed bumps.
Measure and compare clearances between the rear tires. I'd bet they are different by design.
If they are, you can do one of two things: Cut the wheel well out or deal with the rub.
A thicker sway bar in the rear may help control some of the rub on turns, as would stiffer struts/shocks (whichever you have).
