Fortunately, the correction is the same regardless. With sensor banks in front of the robot, skewing to the left has similar sensor readings as perpendicularly offsetting to the left. The correction is steering right for both cases.
When a robot turns (especially in an in-place turn), the top of wall position can be used to help the robot determine when to decelerate and even ``patch'' angular errors. As a robot turns, some sensor will first detect a wall. The robot should slow down the turn because it should know the number of steps to perform.