A theory of absorption and resonance Raman scattering of impurity centers in crystals with E⊗e-type Jahn-Teller effect in the excited state is presented. The vibronic interaction with non-totally symmetric local or pseudolocal modes and with a continuum of bath modes (phonons) is considered. A number of specific quantum effects, such as the nonadiabaticity-induced enhancement of the Raman scattering at high-energy excitation, the size effect of the final state, the interference of different channels of scattering, the Fermi resonances in the conical intersection, and others, were shown to become apparent in the calculated spectra. The vibronic interaction with phonons essentially determines the structure of the spectra.