We show that the initial dynamics of Rayleigh scattering from excitons in quantum wells can be either instantaneous or delayed, depending on the exciton ensemble studied. For excitation of the entire exciton resonance, a finite rise time given by the inverse inhomogeneous broadening of the exciton resonance is observed. Instead, when exciting only a subsystem of the exciton resonance, in our case excitons localized in quantum well regions of a specific monolayer thickness, the rise has an instantaneous component. This is due to the spatial nonuniformity of the initially excited exciton polarization, which emits radiation also into nonspecular directions