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We use high-resolution, hydrodynamic, galaxy simulations from the Latte suite of FIRE-2 simulations to investigate the inherent variation of dark matter in sub-sampled regions around the Solar Circle of a Milky Way-type analogue galaxy and its impact on direct dark matter detection. These simulations show that the baryonic backreaction, as well as the assembly history of substructures, has lasting impacts on the dark matter's spatial and velocity distributions. These are experienced as 'gusts' of dark matter wind around the Solar Circle, potentially complicating interpretations of direct detection experiments on Earth. We find that the velocity distribution function in the galactocentric frame shows strong deviations from the Maxwell Boltzmann form typically assumed in the fiducial Standard Halo Model, indicating the presence of high-velocity substructures. By introducing a new numerical integration technique which removes any dependencies on the Standard Halo Model, we generate event-rate predictions for both single-element Germanium and compound Sodium Iodide detectors, and explore how the variability of dark matter around the Solar Circle influences annual modulation signal predictions. We find that these velocity substructures contribute additional astrophysical uncertainty to the interpretation of event rates, although their impact on summary statistics such as the peak day of annual modulation is generally low.