We present a systematic experimental investigation of an unusual transport phenomenon observed in two-dimensional (2D) electron gases in Si/SiGe heterostructures under integer quantum Hall effect (IQHE) conditions. This phenomenon emerges under specific experimental conditions and in different material systems. It is commonly referred to as a Hall resistance overshoot but it lacks a consistent explanation so far. Based on our experimental findings, we have developed a model that accounts for all of our observations in the framework of a screening theory for the IQHE. Within this model, the origin of the overshoot is attributed to a transport regime where current is confined to co-existing evanescent incompressible strips of different filling factors.