Desalination of seawater by forward osmosis is a technology potentially able to address the global water scarcity problem. The major challenge limiting its widespread practical application is the design of a draw solute that can be separated from water by an energetically efficient process and then reused for the next cycle. Recent experiments demonstrate that a promising draw solute for forward-osmosis desalination is tetrabutylphosphonium 2,4,6-trimethylbenzenesulfonate ([P4444][TMBS]). When mixed with water, this ionic liquid (IL) is thermoresponsive and exhibits a lower critical solution temperature (LCST), above which it phase-separates into an IL-rich phase and a water-rich phase. Elucidating the physical mechanism of the liquid-liquid phase separation, as well as rationally designing optimized derivatives, necessitates an accurate model to describe this and related ILs. In this paper, we resort to explicit-solvent all-atom molecular dynamics simulations and adopt AMBER-based force-field parameters for the cation whose partial charges were assigned by the RESP fitting procedure. Utilizing the same methodology, we parametrize the anion. The simulations' results indicate the IL/water mixture, at the experimental critical composition, can unambiguously phase-separate only when the partial charges of the ions are scaled down. Nevertheless, the best-performing charge scaling factor is found to be 0.95, a value much milder than those reported for ILs in neat phases. This can be explained by a diminished charge transfer, or induced dipoles, within the ions when the IL is in a mixture with water. With this charge scaling, the simulations reproduce well the LCST composition-temperature phase diagram, albeit overestimation of the critical temperature by 10 K. In particular, very good agreement is obtained for the composition of the two segregated phases. Estimation of viscosity points to IL/water mixture that is almost twice as viscous in simulations than that reported experimentally. Furthermore, we analyze changes in energy between different components in the mixture and find that the driving force for phase separation is, at least, enthalpic. Structural analyses of the ions and their interactions with water molecules corroborate the importance of the latter in mediating structural organizations of the anions, as well as in strengthening the interactions between the cations.