I don't think that phonons are that important to explain dispersion of light in the visible region as addressed in this article. Much more important are electronic excitations of the atoms and molecules making up the substance. If these excitations are coupled, one speaks of excitons in analogy to photons. In deed the electrons have a much larger oscillator strength as compared with the phonons.
Although in transparent media like glass, the eigenfrequencies -or rather broad absorption bands - of these modes lie in the ultraviolet region of the spectrum, they can influence the propagation of light in the visible region. The point is that, though nonresonant, the electric field of the light wave can drive forced polarization of the electron clouds. Now ,- well below the resonance frequency - while the phase of the polarisation will be in phase with the driving field, the electric field radiated by the polarisation will lag behind by 90 degrees. This increasing phase lag is nothing else but a reduction of phase velocity.
