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The polarization dependence of nonequilibrium transitions in a multistable cavity-polariton system is studied under a nanosecond long resonant optical excitation at the normal and magic angle incidences with various polarizations of the pump beam. The temporal correlations between the frequency, intensity, and optical polarization of the intra-cavity field, which all undergo sharp threshold-like changes due to the spin dependent interaction of cavity polaritons, are visualized. The observed dynamics cannot be reproduced within the conventional semi-classical model based on the Gross-Pitaevskii equations. To explain the observed phenomena, it is necessary to take into account the unpolarized exciton reservoir which brings on additional blueshift of bright excitons, equal in the σ + and σ − polarization components. This model explains the effect of polarization instability under both pulsed and continuous wave resonant excitation conditions, consistently with the spin ring pattern formation that has recently been observed under Gaussian shaped excitation.