The properties of galaxies with the reddest observed R−K colours [extremely red objects (EROs)], including their apparent division into passive and obscured active objects with roughly similar number densities, are a known challenge for models of galaxy formation. In this paper, we produce mock catalogues generated by interfacing the predictions of the semi‐analytical morgana model for the evolution of galaxies in a Λ cold dark matter cosmology with the spectrophotometric + radiative transfer code grasil and infrared (IR) template library to show that the model correctly reproduces number counts, redshift distributions and active fractions of R−K > 5 sources. We test the robustness of our results against different dust attenuations and, most importantly, against the inclusion of thermally pulsing asymptotic giant branch (TP‐AGB) stars in simple stellar populations used to generate galaxy spectra, and find that the inclusion of TP‐AGBs has a relevant effect in that it allows us to increase by a large factor the number of very red active objects at all colour cuts. We find that though the most passive and the most obscured active galaxies have a higher probability of being selected as EROs, many EROs have intermediate properties and the population does not show bimodality in the specific star formation rate (SSFR). We predict that deep observations in the far‐IR, from 100 to 500 μm, are the most efficient way to constrain the SSFR of these objects; we give predictions for future Herschel observations and show that a few objects will be detected in deep fields at best. Finally, we test whether a simple evolutionary sequence for the formation of z= 0 massive galaxies, going through a sub‐mm‐bright phase and then an ERO phase, is typical in this galaxy formation model. We find that this sequence holds for ∼25 per cent of z= 0 massive galaxies, while the model typically shows a more complex connection between sub‐mm, ERO and massive galaxies.