The optical Kerr effect (OKE) and dielectric relaxation spectroscopy (DRS) signals of MgCl2 aqueous solutions were modeled based on the same group of molecular dynamics simulation trajectories. Plausible agreement between the simulations and the experiments allows us to analyze the microscopic origin of the different concentration dependences of relaxation times probed by these two techniques. Our simulations suggest that a significant amount of cations and anions associate in the solutions due to the ion pairing effect. These ion assemblies as well as the free cations form suspending clusters together with the water molecules in their cation hydration shells. The dynamics of water molecules in these clusters is significantly hindered, while that of other water molecules remains largely unaffected. The relaxation times measured by OKE and DRS have different concentration dependences because DRS probes only the rotational dynamics of water molecules outside of the cluster while OKE contains the information of dynamics of all of the water molecules in the solutions. Such findings provide us a microscopic picture on how the ion hydration affects the water dynamics in certain ionic solutions in which ion pairing plays an important role.