Assemblies of self-rotating particles are gaining interest as a novel realization of active matter with unique collective behaviors such as edge currents and non-trivial dynamic states. Here, we develop a continuum model derived from coarse-grained equations of motions for a system of discrete spinners. We apply the model to explore the mixtures of spinners and same-spin phase separation. We find that the dynamics is strikingly sensitive to fluid inertia: In the inertialess system, after transient turbulent-like motion the spinners segregate and form steady traffic lanes. Contrary, at small but finite Reynolds number, the turbulent-like motion is sustained and the spinner population exhibit a chirality breaking transition: only population with a certain sense of rotation survives. The results shed light on the dynamic behavior of non-equilibrium materials exemplified by active spinners.