We describe the switching process in reversed tilted columnar phase and ferroelectric bistability of polarization-modulated orthogonal smectic liquid crystals (SmAP). The reversed tilted B1 phase is a smectic tilted columnar phase in which the macroscopic polarization can be reorientated via electric field. To study the effects on the reorientation mechanism of the various physical parameters, we analyze a Landau-de Gennes-type energy functional and show how the switching occurs with a relevant role played by the terms that describe the interaction between polarization and nematic directors. In SmAP phase, the opposite anchoring at the stripe boundaries and in-polarization form topological singularities. The free energy of the polarization with electric self-interaction term on one stripe reduces to the Ginzburg-Landau functional with boundary penalty term. We describe the boundary vortices of the reduced functional and obtain convergence results of minimizers. We also perform numerical simulations to illustrate the results of our analysis.