Photoheating associated with reionization suppressed star formation in low-mass galaxies. Reionization was inhomogeneous, however, affecting different regions at different times. To establish the causal connection between reionization and suppression, we must take this local variation into account. We analyze the results of CoDa (‘Cosmic Dawn’) I, the first fully coupled radiation-hydrodynamical simulation of reionization and galaxy formation in the Local Universe, in a volume large enough to model reionization globally but with enough resolving power to follow all atomic-cooling galactic halos in that volume. For every halo identified at a given time, we find the redshift at which the surrounding IGM reionized, along with its instantaneous star formation rate (‘SFR’) and baryonic gas-to-dark matter ratio (⁠|$M_\rm{gas}/M_{\small DM}$|⁠). The average SFR per halo with M < 10^9M_⊙ was steady in regions not yet reionized, but declined sharply following local reionization. For M > 10^10M_⊙, this SFR continued through local reionization, increasing with time, instead. For 10^9M_⊙ < M < 10^10M_⊙, the SFR generally increased modestly through reionization, followed by a modest decline. In general, halo SFRs were higher for regions that reionized earlier. A similar pattern was found for |$M_\rm{gas}/M_{\small DM}$|⁠, which declined sharply following local reionization for M < 10^9M_⊙. Local reionization time correlates with local matter overdensity, which determines the local rates of structure formation and ionizing photon consumption. The earliest patches to develop structure and reionize ultimately produced more stars than they needed to finish and maintain their own reionization, exporting their ‘surplus’ starlight to help reionize regions that developed structure later.