Context. The Centaurs are a transitional population of minor bodies of the solar system and the evolutionary link between the trans-Neptunian objects and the short period comets. The surface properties of these objects are very peculiar, because currently available data suggest that their visual surface colors divide the population into two distinctive groups, those with reddish slopes of the visual reflection spectra and those with neutral spectra. Moreover, some of them are known to posses comas produced by cometary activity. Aims: We aim to investigate possible links between the orbital dynamical history and the surface physical properties of the bodies of this population. Methods: By means of numerical integrations of the equations of motion we calculated the orbital evolution of three groups of Centaurs: the Red group, the Gray group, and the Active group. We looked for statistical differences in the timescales spent by the objects of each group at heliocentric distances below certain values that are associated with locations where certain particular physical processes occur at the surfaces. Results: We find remarkable differences when we compare the fraction of objects that penetrate below typical heliocentric distances for each group. Conclusions: Our results suggest that the observed bimodality in the distribution of surface colors of the Centaurs is caused by the different thermal reprocessing on the surface of bodies of the Red group on one side and the Active and Gray groups on the other. Centaurs of the Gray group likely had cometary activity, therefore their color distribution is similar to that of comet nuclei.