Ionic liquids (ILs) whose water solutions are thermoresponsive provide an appealing route to harvest water from the atmosphere at an energy cost that can be accessed by solar heating. IL/water solutions that present a lower critical solution temperature (LCST), i.e., demix upon increasing temperature, represent the most promising choice for this task since they could absorb vapor during the night when its saturation is highest and release liquid water during the day. The kinetics of water absorption at the surface and the role of nanostructuring in this process have been investigated by atomistic molecular dynamics simulations for the ionic liquid tetrabutyl phosphonium 2,4-dimethylbenzenesulfonate whose LCST in water occurs at Tc = 36 °C for solutions of 50-50 wt % composition. The simulation results show that water molecules are readily adsorbed on the IL and migrate along the surface to form thick three-dimensional islands. On a slightly longer time scale, ions crawl on these islands, covering water and recreating the original surface whose free energy is particularly low. At a high deposition rate, this mechanism allows the fast incorporation of large amounts of water, producing subsurface water pockets that eventually merge into the populations of water-rich and IL-rich domains in the nanostructured bulk. Simulation results suggest that strong nanostructuring could ease the separation of water and water-contaminated IL phases even before macroscopic demixing.