We present discrete and continuum models to describe previous experiments on growth of chemical vapor deposited silica films at 611 K and 723 K [F. Ojeda et al., Phys. Rev. Lett. 84, 3125 (2000)]. Silica films deposited at 723 K show larger surface roughness already from the early stages of growth, a fact that was not explained by a previously proposed phenomenological stochastic equation for the interface height. This larger surface roughness and the concomitant development of higher local slopes seem to be correlated with the Kardar-Parisi-Zhang asymptotic scaling observed for the high-temperature conditions. Here, we explain these features on the basis of surface heterogeneity and short-range memory effects, which are assessed for our experimental system through spectroscopic measurements. By incorporating these effects into a random deposition model and related Langevin equations with correlated noise, we are able to account for the full set of experimental observations.