Establishing the evolutionary timescales of the massive star formation process through chemistry

(Abridged) Understanding the details of the formation process of massive (i.e. M<8-10M$_\odot$) stars is a long-standing problem in astrophysics. [...] We present a method to derive accurate timescales of the different evolutionary phases of the high-mass star formation process. We model a representative number of massive clumps of the ATLASGAL-TOP100 sample which cover all the evolutionary stages. The models describe an isothermal collapse and the subsequent warm-up phase, for which we follow their chemical evolution. The timescale of each phase is derived by comparing the results of the models with the properties of the sources of the ATLASGAL-TOP100 sample, taking into account the mass and luminosity of the clumps, and the column densities of methyl acetylene (CH$_3$CCH), acetonitrile (CH$_3$CN), formaldehyde (H$_2$CO) and methanol (CH$_3$OH). We find that the chosen molecular tracers are affected by the thermal evolution of the clumps, showing steep ice evaporation gradients from 10$^3$ to 10$^5$ AU during the warm-up phase. We succeed in reproducing the observed column densities of CH$_3$CCH and CH$_3$CN, while H$_2$CO and CH$_3$OH show a poorer agreement with the observed values. The total (massive) star formation time is found to be $\sim5.2\times10^5$ yr, which is defined by the timescales of the individual evolutionary phases of the ATLASGAL-TOP100 sample: $\sim5\times10^4$ yr for 70-$\mu$m weak, $\sim1.2\times10^5$ yr for mid-IR weak, $\sim2.4\times10^5$ yr for mid-IR bright and $\sim1.1\times10^5$ yr for HII-regions phases. Our models, with an appropriate selection of molecular tracers that can act as chemical clocks, allow to get robust estimates of the duration of the individual phases of the high-mass star formation process, with the advantage of being capable to include additional tracers aimed at increasing the accuracy of the estimated timescales.