Recent TCV experiments confirm the predicted formation of an electric potential well, below the magnetic X-point, in configurations with unfavorable $B_t$ field direction (ion $\nabla B$ drift away from the divertor), that substantially reshapes the typical divertor $E\times B$ flow pattern. The local charge balance $\nabla \cdot j=0$ in the private flux region (PFR) of diverted tokamak plasmas has been previously argued to be dominated by parallel and diamagnetic currents. This hypothesis is tested herein in TCV discharges by comparison with SOLPS-ITER simulations, fully accounting for drifts and currents. Simulated parallel currents correctly capture measured current profile characteristics for both targets and both -directions, whereas those omitting drifts fail. It is shown that the resulting parallel currents dictate the electric fields in the PFR for low temperature (detached divertor) conditions resulting in locally negative electric plasma potential in configurations with unfavorable H-mode access.