The problem with overfilling the reservoir is that as the fluid heats up and expands it is going to be expelled through the vent. If you notice on the little dipstick on the cap, there usually is a ‘cold’ level and a ‘hot’ level. So if the reservoir was filled to the brim the equivalent amount of fluid between the ‘cold’ and ‘hot’ lines would have been expelled. If the reservoir is near the belt or power steering pully, the fluid may have gotten on the belt causing it to slip. If this has happened clean the pulleys (engine not running) and clean or replace the belt.
Let us know what you finally find.