The time-dependent fluorescence Stokes shift monitors the relaxation of the polarization of a polar solvent in the surroundings of a photoexcited solute molecule but also the structural variation of the solute following photoexcitation and the subsequent molecular charge redistribution. Here, we formulate a simple nonequilibrium quantum theory of solvation for an explicitly time-dependent continuous solvent. The time-dependent solvent induces nonequilibrium fluctuations on the solvent dynamics which are directly reflected in different time components in the time-dependent Stokes shift. We illustrate the structural dynamics in the presence of an explicitly time-dependent solvent by the example of a dynamically shrinking solute which leads to a bimodal Stokes shift. Interestingly, both contributions are mutually coupled. Furthermore, we can explain a prominent long-tail decay of the Stokes shift associated with slow structural dynamical variations.