Out-of-equilibrium molecular systems hold great promise as dynamic, reconfigurable matter that executes complex tasks autonomously. However, translating molecular scale dynamics into spatiotemporally controlled phenomena at mesoscopic length scales remains a challenge. In living cells, reliable positioning processes such as the centering of the centrosome involve forces that result from dissipative self-assembly. We demonstrate how spatiotemporal positioning emerges in synthetic systems where self-assembly is coupled to molecular fluxes originating from concentration gradients. At the core of our system are millimeter long self-assembled filaments and Marangoni flows induced by non-uniform amphiphile distributions. We demonstrate how repulsive and attractive forces that are generated as filaments organize between source and drain droplets sustain autonomous positioning of dynamic assemblies at the mesoscale. Our concepts provide a new paradigm for the development of non-equilibrium matter with spatiotemporal programmability.