The unsteady vortical flows and separation-induced transition over a 2-bladed cycloidal rotor are investigated numerically at two advance coefficients, with special emphasis on the influence of two different turbulence models, namely the original SST k-ω model and SST γ-Reθt transition model. Firstly, the applicability of the transition model in predicting the transitional flows over a single airfoil at different incidences is evaluated, and the main results show a good agreement with the experiments, in terms of the mean pressure coefficients and transition locations. Then, the global performance and detailed internal flow structures of the cycloidal rotor are also used to compare with the existing numerical and experimental data. The primary results show that increasing the advanced coefficient can’t change the transition location of the performance of the single blade, but the magnitudes of these variables (vertical force, propulsive force and power coefficients). Then, combining the forces (lift and drag) acting on two blades, the blade loadings and the detailed near-wall flows, the difference of the vertical force and propulsive force of the rotating system and single blade are clarified clearly for two turbulence models. Finally, at advancing side, the transition and its evolution on a single blade is elaborated. It shows that the SST γ-Reθt transition model is superior in predicting the overall performance, but is highly subjected to the disturbances, characterized by the large-scale vortex structures and massive flow separation, compared with SST k-ω model. Simultaneously, it has the capability to capture the transition process, from growing waves of the laminar boundary layer induced by the roll-up vortices to the fully generation of the separation bubble. It believes that this work can deepen the understandings of underlying flow physics inside the cycloidal rotor at low Reynolds number.