The current study investigates the Stefan number effect on the transition from stationary to oscillatory convection in a rotating mushy layer where the near eutectic approximation is applied. It is found that for rotating solidifying systems exhibiting a Stefan number of unit order (i.e., St = 1), stationary convection is only possible up to Ta = 3. Beyond Ta = 3, for St = 1, it is found that the oscillatory mode is the most dangerous mode of convection. A map showing the region of occurrence of the oscillatory mode is also presented for a range of Stefan numbers. The map reveals that the oscillatory mode is the most dangerous mode for intermediate values of Stefan number whilst the stationary mode is the most dangerous mode for very small and very large values of Stefan number. It is also demonstrated that increasing the rotation rate serves to render the oscillatory mode as the becoming the most dangerous mode of convection.