Microwave pumped spin-wave instabilities in YIG spheres were one of the first experimental systems used to demonstrate that chaos can be suppressed by small periodic modulations in an accessible system parameter. Here we show that the equations describing two interacting spin-wave modes account satisfactorily for the experimental results, as long as the field modulation is appropriately introduced in the model. The finite detuning parameters expressing the boundary conditions of the sample provide a natural way for introducing the field modulation. Thus the present results constitute additional evidence of the validity of the two-mode model with momentum-nonconserving driving Hamiltonian used to explain the sample size dependence of the self-oscillations.