We present a Bayesian full-spectral-fitting analysis of 75 massive ($M_* > 10^{10.3} M_odot$) UVJ-selected galaxies at redshifts of $1.0 < z < 1.3$, combining extremely deep rest-frame ultraviolet spectroscopy from VANDELS with multi-wavelength 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 firstly constrain the stellar mass vs stellar age relationship, finding a steep trend towards earlier average formation with increasing stellar mass of $1.48^{+0.34}_{-0.39}$ Gyr per decade in mass, although this shows signs of flattening at $M_* > 10^{11} M_odot$. 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 ($M_* sim 10^{10.5} M_odot$) are consistent with formation in recent ($z<2$), intense starburst events, with timescales of $lesssim500$ 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 $zsim5$ and quenched by $z=3$. However, we find evidence for their continued evolution through both AGN and rejuvenated star-formation activity.
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