The Vlasiator hybrid‐Vlasov code was developed to investigate global magnetospheric dynamics at ion‐kinetic scales. Here we focus on the role of magnetic reconnection in the formation and evolution of magnetic islands at the low‐latitude magnetopause, under southward interplanetary magnetic field conditions. The simulation results indicate that (1) the magnetic reconnection ion kinetics, including the Earthward pointing Larmor electric field on the magnetospheric side of an X‐point and anisotropic ion distributions, are well‐captured by Vlasiator, thus enabling the study of reconnection‐driven magnetic island evolution processes, (2) magnetic islands evolve due to continuous reconnection at adjacent X‐points, “coalescence” which refers to the merging of neighboring islands to create a larger island, “erosion” during which an island loses magnetic flux due to reconnection, and “division” which involves the splitting of an island into smaller islands, and (3) continuous reconnection at adjacent X‐points is the dominant source of magnetic flux and plasma to the outer layers of magnetic islands resulting in cross‐sectional growth rates up to + 0.3 RE2/min. The simulation results are compared to the Magnetospheric Multiscale (MMS) measurements of a chain of ion‐scale flux transfer events (FTEs) sandwiched between two dominant X‐lines. The MMS measurements similarly reveal (1) anisotropic ion populations and (2) normalized reconnection rate ~0.18, in agreement with theory and the Vlasiator predictions. Based on the simulation results and the MMS measurements, it is estimated that the observed ion‐scale FTEs may grow Earth‐sized within ~10 min, which is comparable to the average transport time for FTEs formed in the subsolar region to the high‐latitude magnetopause. Future simulations shall revisit reconnection‐driven island evolution processes with improved spatial resolutions.