Many intermediate-age star clusters in the Magellanic Clouds present multiple main-sequence turn-offs (MMSTOs), which challenge the classical idea that star formation in such objects took place over short time-scales. It has been recently suggested that the presence of fast rotators among main-sequence stars could be the cause of such features, hence relaxing the need for extended periods of star formation. In this Letter, we compute evolutionary tracks and isochrones of models with and without rotation. We find that, for the same age and input physics, both kinds of models present turn-offs with an almost identical position in the colour–magnitude diagrams (CMDs). As a consequence, a dispersion of rotational velocities in coeval ensembles of stars could not explain the presence of MMSTOs. We construct several synthetic CMDs for the different kinds of tracks and combinations of them. The models that best reproduce the morphology of observed MMSTOs are clearly those assuming a significant spread in the stellar ages – as long as ∼400 Myr – added to a moderate amount of convective core overshooting. Only these models produce the detailed ‘golf club’ shape of observed MMSTOs. A spread in rotational velocities alone cannot do anything similar. We also discuss models involving a mixture of stars with and without overshooting, as an additional scenario to producing MMSTOs with coeval populations. We find that they produce turn-offs with a varying extension in the CMD direction perpendicular to the lower main sequence, which are clearly not present in observed MMSTOs.