We study the effect of a uniform external magnetization on p-wave superconductivity on the (001) surface of the crystalline topological insulator(TCI) Pb$_{1-x}$Sn$_{x}$Te. It was shown by us in an earlier work that a chiral p-wave finite momentum pairing (FFLO) state can be stabilized in this system in the presence of weak repulsive interparticle interactions. In particular, the superconducting instability is very sensitive to the Hunds interaction in the multiorbital TCI, and no instabilities are found to be possible for the wrong sign of the Hunds splitting. Here we show that for a finite Hunds splitting of interactions, a significant value of the external magnetization is needed to degrade the surface superconductivity, while in the absence of the Hunds interaction, an arbitrarily small external magnetization can destroy the superconductivity. This implies that multiorbital effects in this system play an important role in stabilizing electronic order on the surface.
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