The dynamic solvation time correlation function X(t) is, within linear response, formulated in terms of the intermolecular solute-solvent interactions, without recourse to the intrinsically macroscopic concept of a cavity carved out of a dielectric medium. For interaction site models (ISM) of both the solute and the solvent, the theory relates the fluctuating polarization charge density of the solvent to the fluctuating vertical energy gap that controls X(t). The theory replaces the factual (or bare) solute charge distribution by a surrogate expressed in terms of the solute-solvent site-site direct correlation functions. Calculations for solute ions in water and in acetonitrile lead to X(t) and the second moment of the associated spectral density in good agreement with molecular-dynamics Simulation results in the literature. We also use the theory to calculate X(t) for model solutes in which the "sudden" change of the charge distribution involves multipoles of higher order. The response is qualitatively similar in the various cases studied here.