The absorption and resonance Raman spectra have been investigated for the first excited state of the julolidinemalononitrile push-pull chromophore in cyclohexane, dichloromethane, and acetonitrile by means of time dependent density functional theory calculations. The effect of nonlocal exchange has been considered by using three different hybrid exchange-correlation functionals containing 20%, 35%, and 50% of exact Hartree-Fock exchange. The interactions with the solvent have been described by the polarizable continuum model. The short-time approximation expression has been used to evaluate the resonance Raman intensities, while the vibronic theory of resonance Raman spectroscopy has been employed to determine both the intensities and the excitation profiles. It is shown that a consistent description of the vibronic structure of the excited state and resonance Raman spectra can be obtained provided that an adequate amount, close to 35%, of exact exchange is included in the exchange-correlation functional. The effect of increasing the polarity of the solvent is well represented by the polarizable continuum, model, both for the absorption spectra and resonance Raman intensities. In particular, these simulations can reproduce the observed variations of the 1560 cm-1 band intensity and attribute them to elongations of a CC double bond upon electronic excitation. Moreover, the short-time approximation has been found sufficient to reproduce most of the results of the more evolved vibronic theory of resonance Raman spectroscopy, which includes summations over vibrational excited states, for both the spectral signatures and their solvent dependencies.