We present results of modelling the broad-band spectral energy distribution (SED) and multiwavelength variability of the bright flat spectrum radio quasars PKS 1510−089 with our time-dependent multizone Monte Carlo/Fokker–Planck code. As the primary source of seed photons for inverse Compton scattering, we consider radiation from the broad-line region (BLR), from the hot dust of the molecular torus and the local synchrotron radiation [synchrotron self-Compton (SSC)]. We evaluate the viability of different Compton models by comparing simulated multiwavelength light curves and SEDs with one of the best observed flares by PKS 1510−089, in 2009 March. The time dependence of our code and its correct handling of light travel time effects allow us to fully take into account the effect of the finite size of the active region, and in turn to fully exploit the information carried by time-resolved observed SEDs that are becoming increasingly available since the launch of Fermi. We confirm that the spectrum adopted for the external radiation field has an important impact on the modelling of the SED, in particular for the lower energy end of the Compton component which is observed in the X-ray band, which in turn is one of the most critical bands to assess the differences between external Compton and SSC emission. In the context of the scenario presented in this paper, where the flaring is caused by the increase of the number of relativistic electrons ascribed to the effect of the interaction of a portion of the jet (blob) with a shock, we cannot firmly discriminate the three main scenarios for γ-ray emission. However, results show clearly the differences produced by a more realistic treatment of the emitting source in the shape of SEDs and their time variability over relevant, observable time-scales, and demonstrate the crucial importance of time-dependent multizone models to advance our understanding of the physics of these sources, by taking full advantage of the wealth of information offered by the high-quality data of current multiwavelength campaigns.