This work explores the role of small-scale environment (< 1 Mpc) in modulating accretion events onto supermassive black holes by studying the incidence of Active Galactic Nuclei (AGN) in massive clusters of galaxies. A flexible, data-driven semi-empirical model is developed based on a minimal set of parameters and under the zero order assumption that the incidence of AGN in galaxies is independent of environment. This is used to predict how the fraction of X-ray selected AGN among galaxies in massive dark matter halos (\(\gtrsim 3 \times 10^{14}\,\rm{M}_{\odot}\) ) evolves with redshift and reveal tensions with observations. At high redshift, \(z\sim1.2\), the model underpredicts AGN fractions, particularly at high X-ray luminosities, \(L_X(\rm 2-10\,keV) \gtrsim 10^{44}\, erg \, s^{-1}\). At low redshift, \(z\sim0.2\), the model estimates fractions of moderate luminosity AGN (\(L_X(\rm 2-10\,keV) \gtrsim 10^{43}\, erg \, s^{-1}\)) that are a factor of 2-3 higher than the observations. These findings reject the zero order assumption on which the semi-empirical model hinges and point to a strong and redshift-dependent influence of the small-scale environment on the growth of black holes. Cluster of galaxies appear to promote AGN activity relative to the model expectation at \(z\sim1.2\) and suppress it close to the present day. These trends could be explained by the increasing gas content of galaxies toward higher redshift combined with an efficient triggering of AGN at earlier times in galaxies that fall onto clusters.