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Dissipative Kerr soliton microcombs in microresonators has enabled fundamental advances in chip scale precision metrology, communication, spectroscopy, and parallel signal processing. Here we demonstrate polarization diverse soliton transitions and deterministic switching dynamics of a self stabilized microcomb in a strongly coupled dispersion-managed microresonator driven with a single pump laser. The switching dynamics are induced by the differential thermorefractivity between coupled transverse magnetic and transverse electric supermodes during the forward backward pump detunings. The achieved large soliton existence range and deterministic transitions benefit from the switching dynamics, leading to the cross polarized soliton microcomb formation when driven in the transverse magnetic supermode of the single resonator. Resultantly the pump laser always exists at the effective blue detuning of the transverse magnetic resonance, fundamentally mitigating the thermal destabilization barrier and improving accessibility of the soliton formation regime. Subsequently and secondly, we demonstrate two distinct polarization diverse soliton formation routes arising from chaotic or periodically modulated waveforms via pump power selection. The generated self stabilized supermode microcomb features an extraordinarily large soliton existence range, a variety of soliton state transitions with well defined pump laser tuning, high pump microcomb conversion efficiency, and low repetition rate phase noise.