A growing number of experimental and theoretical works have been addressing various aspects of the viscous fingering formation in rotating Hele-Shaw cells. However, only a few of them consider the influence of Coriolis forces. The studies including Coriolis effects are mostly restricted to the high-viscosity-contrast limit and rely on either purely linear stability analyses or intensive numerical simulations. We approach the problem analytically and use a modified Darcy's law including the exact form of the Coriolis effects to execute a mode-coupling analysis of the system. By imposing no restrictions on the viscosity contrast A (dimensionless viscosity difference) we go beyond linear stages and examine the onset of nonlinearities. Our results indicate that when Coriolis effects are taken into account, an interesting interplay between the Reynolds number Re and A arises. This leads to important changes in the stability and morphological features of the emerging interfacial patterns. We contrast our mode-coupling approach with previous theoretical models proposed in the literature.