The exact quantum time-dependent optical response of hydrogen under strong-field near-infrared excitation is investigated and compared to the perturbative model widely used for describing the effective atomic polarization induced by intense laser fields. By solving the full 3D time-dependent Schrödinger equation, we exhibit a supplementary, quasi-instantaneous defocusing contribution missing in the weak-field model of polarization. We show that this effect is far from being negligible, in particular when closures of ionization channels occur and stems from the interaction of electrons with their parent ions. It provides an interpretation of the higher-order Kerr effect recently observed in various gases.