ABSTRACT We present a Bayesian full-spectral-fitting analysis of 75 massive ($M_* \gt 10^{10.3} \, \mathrm{M_\odot }$) UVJ-selected galaxies at redshifts of 1.0 < z < 1.3, combining extremely deep rest-frame ultraviolet spectroscopy from VANDELS with multiwavelength photometry. By the use of a sophisticated physical plus systematic uncertainties model, constructed within the bagpipes code, we place strong constraints on the star-formation histories (SFHs) of individual objects. We first constrain the stellar mass versus stellar age relationship, finding a steep trend towards earlier average formation time with increasing stellar mass (downsizing) of $1.48^{+0.34}_{-0.39}$ Gyr per decade in mass, although this shows signs of flattening at $M_* \gt 10^{11} \, \mathrm{M_\odot }$. We show that this is consistent with other spectroscopic studies from 0 < z < 2. This relationship places strong constraints on the AGN-feedback models used in cosmological simulations. We demonstrate that, although the relationships predicted by simba and illustristng agree well with observations at z = 0.1, they are too shallow at z = 1, predicting an evolution of ≲0.5 Gyr per decade in mass. Secondly, we consider the connections between green-valley, post-starburst, and quiescent galaxies, using our inferred SFH shapes and the distributions of galaxy physical properties on the UVJ diagram. The majority of our lowest-mass galaxies ($M_* ∼ 10^{10.5} \, \mathrm{M_\odot }$) are consistent with formation in recent (z < 2), intense starburst events, with time-scales of ≲500 Myr. A second class of objects experience extended star-formation epochs before rapidly quenching, passing through both green-valley and post-starburst phases. The most massive galaxies in our sample are extreme systems: already old by z = 1, they formed at z ∼ 5 and quenched by z = 3. However, we find evidence for their continued evolution through both AGN and rejuvenated star-formation activity.