Despite the emerging morphological evidence that luminous quasar-like active galactic nuclei (AGN) are triggered in galaxy mergers, the natures of the triggering mergers and the order of events in the triggering sequence remain uncertain. In this work, we present a detailed study of the stellar populations of the host galaxies of 21 type II quasars, with the aim of understanding the sequence of events between the onset of the merger, the triggering of the associated starburst and the initiation of the quasar activity. To this end, we model high-quality, wide spectral coverage, intermediate-resolution optical spectra of the type II quasars. We find that of the 21 objects, the higher order Balmer absorption lines, characteristic of young stellar populations (YSPs), are directly detected in similar to 62 per cent of the sample. We also fit these spectra using a number of combinations of stellar and/or power-law components, representative of viable formation histories, as well as including the possibility of scattered AGN light. We find that similar to 90 per cent of the type II quasar host galaxies require the inclusion of a YSP to adequately model their spectra, whilst 71 per cent of the sample require the inclusion of a YSP with age <100 Myr. Since the ages of the YSP in most type II quasar host galaxies are comparable with the expected lifetimes of the AGN activity, these results provide strong evidence that the quasars are triggered close to the peaks of the merger-induced starbursts.