Polarization instability (PI) of ultrashort light pulses, giving rise to vectorial supercontinuum generation, is demonstrated using a subwavelength-core, highly birefringent, normally dispersive optical fiber. The evolution of ultrashort pulses in the regime of PI is shown to radically differ from polarization-instability dynamics of cw fields and longer laser pulses. As the peak power of the laser field decreases along the propagation path due to dispersion-induced pulse stretching, the Poincaré-sphere map of field dynamics is shown to evolve from the behavior typical of PI in the highly nonlinear regime toward the beating dynamics of uncoupled polarization modes, characteristic of low field intensities and cw fields.