Recent solvation dynamics experiments with common dipolar solvation probes in imidazolium room temperature ionic liquids (RTIL) have revealed large dynamic Stokes' shifts and biphasic solvation energy relaxations. Because of the dipolar nature of the imidazolium cations, the solute-cation (dipole-dipole) interaction may, in addition to the ion-solute (ion-dipole) interaction, Contribute significantly to the observed Stokes' shift and its dynamics. Conventional time-resolved measurements, however, cannot separate out these contributions. A simple semimolecular theory is described here which, upon separation of the dipolar part of the solvation energy from the ion-dipole part, allows estimation of these two components in the measured shifts. While the sum-total of these separated out components agree well with experiments, the ion-dipole interaction is found to contribute similar to 60% of the measured shift in each of these dipolar RTILs. In addition, the calculated solvation response functions, as observed in experiments, are characterized by a fast exponential component (similar to 15-20%) with a time constant in the subpicosecond regime and a slow nonexponential component with a Little constant in the subnanosecond regime. Interestingly, the present theory finds that the fast component of the solvation response function in imidazolium ionic liquids originates from the rapid orientational relaxation involving the dipolar species in these liquids, whereas the relaxation of the ion dynamic Structure factor via ion translation produces the observed slow nonexponential component. In addition, calculations presented here explain why the continuum model based theories of solvation dynamics do not work for these liquids. For alkylphosphonium ionic liquids, the ion-dipole interaction accounts for nearly 75% of the measured shifts. The present theory also explains why the experimentally observed solvation response function in these liquids does not contain any subpicosecond component and decays nonexponentially with only a single relaxation time constant.