By resorting to a novel implementation of the first-principles-based van der Waals correction (vdWC) based on maximally localized Wannier functions (MLWFs), we inspect its performance and assess its reliability for aqueous solutions of alkali metal ions. In our implementation of vdWCs, an efficient extrapolation scheme is introduced to allow for affordable first principles molecular dynamics avoiding the explicit recalculation of MLWFs at each step. We find that vdWCs, when added to the widely used revPBE gradient corrected functional, influence substantially both structural and dynamical properties of water molecules, with particular emphasis on the hydration shell of the alkali cations. These effects are more evident for strong structure-making and -breaking cationic species. Moreover, self-diffusion coefficients and reorientation correlation times of solvating water molecules change systematically, showing a trend in better agreement with experiments with respect to simulations neglecting the long-range dispersion contributions.