The laser-assisted holographic grating recording process in films of azobenzene functionalized polymers is usually studied by observation of the efficiency of light scattering on a developing in time diffraction grating. Various possible mechanisms contributing to grating formation as well as the bulk or surface origin (bulk refractive index and/or relief grating) of light scattering make the analysis of kinetics of grating recording, from the light scattering data only, difficult and ambiguous. To fully explain experimentally observed various and complex (frequently nonexponential) kinetics of the first-order light diffraction intensity, we considered a simple single-exponential growth of the two phase gratings in the same polymer film. In modeling we assumed that the bulk refractive index grating Delta n(t) and the surface relief grating Delta d(t) differ considerably in their growth rates and we allowed for a nonstationary phase shift Delta phi(t) between them which was experimentally observed during the recording process. The origin of the nonstationary phase shift is a result of a slow shift of interference pattern due to delicate symmetry breaking in illumination conditions (e.g., difference in beam intensities and deviation of exact symmetrical beam incidence angles on the sample). Changing only such parameters as stationary amplitudes of refractive index and relief gratings for a span of phase shifts (0-pi) between them, we obtained a series of kinetic responses which we discuss and interpret. The various examples of temporal evolution of diffraction efficiency for the same grating formation kinetics, modeled in our work, supply evidence that great care must be taken to properly interpret the experimental results.