Thanks to Integral Field Unit survey data, it is possible to explore in detail the link between the formation of the stellar content in galaxies and the drivers of evolution. Traditionally, scaling relations have connected galaxy-wide parameters such as stellar mass (M$_s$), morphology or average velocity dispersion ($\sigma$) to the star formation histories (SFHs). We study a high quality sample of SDSS–MaNGA spectra to test the possibility that sub-galaxy ($\lesssim$2 kpc) scales are dominant, instead of galaxy-wide parameters. We find a strong correlation between local velocity dispersion and key line strengths that depend on the SFHs, allowing us to make the ansatz that this indicator – that maps the local gravitational potential – is the major driver of star formation in galaxies, whereas larger scales play a role of a secondary nature. Galactocentric distance has a weaker correlation, suggesting that the observed radial gradients effectively reflect local variations of velocity dispersion. In our quest for a cause, instead of a correlation, we contrast $\sigma$ with local stellar mass (or surface mass density), that appears less correlated with population properties. We conclude that the inherently higher uncertainty in M$_s$ (or $\Sigma _M$)may explain its lower correlation with respect to $\sigma$, but the extra uncertainty needed for $\sigma$ to have similar correlations as stellar mass is rather high. Therefore, we posit local velocity dispersion as the major driver of evolution, a result that should be reproduced by hydrodynamical models at the proper resolution.