Time-resolved up-conversion measurements of secondary emission from multiple quantum wells under resonant femtosecond excitation are reported for GaAs multiple quantum wells with qualitatively different interface disorder. The transient resonant Rayleigh scattering presents very peculiar features such as a long-lived signal and a nonmonotonic behaviour, which cannot be explained by a classical model. A microscopic model is proposed, where the quantum mechanical equation for the microscopic polarization is solved numerically assuming a random two-dimensional potential with spatial correlation, and a phenomenological dephasing time. The model succeeds in reproducing the shape of the transients. It is shown that, for typical parameters of GaAs quantum well excitons, quantum mechanical features are essential in the description of the scattered intensity. The observed features of the signal are interpreted in terms of polarization beatings due to the energy quantization of exciton levels lying within the same fluctuation site.