Ionic liquid-water binary solutions have significantly expanded the applications of ionic liquids (ILs) in chemical and biological research. Therefore, considerable research has focused on measuring the thermophysical properties of these binary mixtures. From low-to-moderate concentrations of water, several IL/water mixtures exhibit deviations from expected trends in thermophysical behavior. One such example is a unique density trend observed for certain IL classes, which exhibit a characteristic increase in density with the addition of small amounts of water. Since water primarily interacts with the IL anion, such deviations have always been explained in the context of anion-water associations. Surprisingly, however, IL/water mixtures containing different cations but a common lactate anion exhibit similar peculiarities in density trends. Using atomistic level molecular dynamics simulations, we show that diverse density trends are caused by cation-mediated modulations in the IL nanostructure. Depending on its nature, the IL cation can play a dual role in modulating the IL nanostructure: (i) resist water-mediated breakdown of the nanostructure by interacting with the anion very strongly, (ii) further strengthen the nanostructure by incorporating water in the IL framework. The [emim] cation fails to play both roles resulting in the density decrease, while the [tmg] cation fulfills both roles leading to a density rise. The choline cation resists the density fall by inducing the formation of "water-clathrates" in the solution. Such occurrence of clathrates in IL/water binary mixtures, reported for the first time in this study, further emphasizes that the properties of ILs and its mixtures are not merely determined by the chemical nature of the component ions, but also by their unique nanostructural organizations. These unique nanostructural organizations also manifest in their unusual dynamics.