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We investigate phase separation in a chiral fluid, made of spinning ferromagnetic colloids that interact both via hydrodynamic and dipolar forces and collectively organize into separated circulating clusters. We show that, at high spinning frequency, hydrodynamics dominate over attractive magnetic interactions and impede coarsening, forcing the particles to assemble into a collection of finite rotating clusters of controllable size. We introduce a minimal particle-based model that unveils the fundamental role of hydrodynamics and the boundary plane in the self-organization process of the colloidal spinners. Our results shed light on the control of coarsening and dynamic self-assembly in chiral active systems and the key role played by fluid mediated long-range interactions.