Hierarchical compartmentalization, a hallmark of both primitive and modern cells, enables the concentration and isolation of biomolecules, and facilitates spatial organization of biochemical reactions. Coacervate-based compartments can sequester and recruit a large variety of molecules, making it an attractive protocell model. In this work, we report the spontaneous formation of core-shell cell-sized coacervate-based compartments driven by spontaneous evaporation of a sessile droplet on a thin-oil-coated substrate. Our analysis reveals that such far-from-equilibrium architectures arise from multiple, coupled segregative and associative liquid-liquid phase separation, and are stabilized by stagnation points within the evaporating droplet. The formation of stagnation points results from convective capillary flows induced by the maximum evaporation rate at the liquid-liquid-air contact line. This work provides valuable insights into the spontaneous formation and maintenance of hierarchical compartments under non-equilibrium conditions, offering a glimpse into the real-life scenario.