Galaxy evolution is driven by a variety of physical processes which are predicted to proceed at different rates for different dark matter haloes and environments across cosmic times. A record of this evolution is preserved in galaxy stellar populations, which we can access using absorption-line spectroscopy. Here we explore the large LEGA-C survey (DR3) to investigate the role of the environment and stellar mass on stellar populations at z~0.6-1.0 in the COSMOS field. Leveraging the statistical power and depth of LEGA-C, we reveal significant gradients in D4000 and H-delta equivalent widths (EWs) distributions over the stellar mass vs environment 2D spaces for the massive galaxy population (M>10^10 M$_{\odot}$) at z~0.6-1.0. D4000 and H-delta EWs primarily depend on stellar mass, but they also depend on environment at fixed stellar mass. By splitting the sample into centrals and satellites, and in terms of star-forming galaxies and quiescent galaxies, we reveal that the significant environmental trends of D4000 and H-delta EW when controlling for stellar mass are driven by quiescent galaxies. Regardless of being centrals or satellites, star-forming galaxies reveal D4000 and H-delta EWs which depend strongly on their stellar mass and are completely independent of the environment at 0.6< z < 1.0. The environmental trends seen for satellite galaxies are fully driven by the trends that hold only for quiescent galaxies, combined with the strong environmental dependency of the quiescent fraction at fixed stellar mass. Our results are consistent with recent predictions from simulations that point toward massive galaxies forming first in overdensities or the most compact dark matter haloes.