Are you saying that you had a bike shop "tune" your bike, and that it can still overshift on one side of the rear cogs? Take it back to them. There are two screws on each derailleur that are adjusted to limit travel to just meet the outer and inner alignment points. The bike shop should have checked these first.
As for cleaning, unless you paid the shop for this, any cleaning that they did is a benefit to you. You should keep your bike clean and well lubricated on your own. It's part of operation, just like pumping up the tires.