Solution-cast, thin-film polymer composites find a wide range of applications, such as in the photoactive layer of organic solar cells. The performance of this layer crucially relies on its phase-separated morphology. Efficient charge-carrier extraction requires each of the components to preferentially wet one of the two electrodes. It is often presumed that the experimentally observed surface enrichment required for this is caused by specific interactions of the active ingredients with each surface. By applying a generalized diffusion model, we find the dynamics to also play an important role in determining which component accumulates at which surface. We show that for sufficiently fast evaporation the component with the smallest cooperative diffusivity accumulates at the free interface. Counterintuitively, depending on the interactions between the various components, this may be the smaller solute. Our comprehensive numerical and analytical study provides a tool to predict and control phase-separated morphologies in thin-film polymer composites.