The uniform theory of photoemission of a dissociating molecule excited by a laser pulse is developed. It is shown that transient effects lead to the appearance of additional terms, not included in the Kramers-Heisenberg formula. The role of ''true'' Raman scattering vs ''resonance fluorescence'' in contributing to the observed signal is elucidated. It is shown that the relative importance of these two processes is strongly dependent on the pulse parameters and the radiative lifetimes. ''True' Raman is shown to dominate at very short times, during the rise of the pulse. At longer times resonance fluorescence sets in and dominates the observed signal. Computations based on the above theory of the time-averaged excitation-emission spectrum (the emission signal as a function of the excitation wavelength) of CH3I with real nanosecond pulses are presented. The present study explains the rich structure observed experimentally and points out ways of translating this structure to 'real-time' information.