Couplings between biochemical and mechanical processes have a profound impact on embryonic development. However, in-vitro studies capable of quantifying these interactions have remained elusive. Here, we investigate a synthetic system where a DNA reaction-diffusion (RD) front is advected by a turbulent flow generated by active matter (AM) flows in a quasi-one-dimensional geometry. Whereas the dynamics of simple RD fronts solely depend on the reaction and diffusion rates, we show that RD-AM front propagation is also influenced by the confinement geometry. We first experimentally dissected the different components of the reaction-diffusion-advection process by knocking out reaction or advection and observed how RD-AM allows for faster transport over large distances, avoiding dilution. We then show how confinement impacts active matter flow: while changes in instantaneous flow velocities are small; correlation times are dramatically increased with decreasing confinement. As a result, RD-AM front speed increased 3 to 9-fold compared to a RD one. This RD-AM experimental model provides a framework for the rational engineering of complex spatiotemporal processes observed in living systems. It will reinforce our understanding of how macro-scale patterns and structures emerge from microscopic components in non-equilibrium systems.