Strong-field ionization (SFI) is a key process for accessing real-time quantum dynamics of electrons on the attosecond timescale. The theoretical foundation of SFI was pioneered in the 1960s, and later refined by various analytical models. While asymptotic ionization rates predicted by these models have been tested to be in reasonable agreement for a wide range of laser parameters, predictions for SFI on the sub-laser-cycle timescale are either beyond the scope of the models or show strong qualitative deviations from full quantum-mechanical simulations. Here, using the unprecedented state specificity of attosecond transient absorption spectroscopy, we follow the real-time SFI process of the two valence spin-orbit states of xenon. The results reveal that the irreversible tunnelling contribution is accompanied by a reversible electronic population that exhibits an observable spin-orbit-dependent phase delay. A detailed theoretical analysis attributes this observation to transient ground-state polarization, an unexpected facet of SFI that cannot be captured by existing analytical models that focus exclusively on the production of asymptotic electron/ion yields.