The penetration of the magnetic field in a rotating inhomogeneous plasma is investigated with direct numerical simulations. The main focus of this work is to test the linear, singular-layer models when diamagnetic and finite Larmor radius effects are included. Our results confirm the existing analytical prediction when the plasma velocity at the resonant surface is outside the drift band, which is the band bounded by the electric drift velocity and the electron diamagnetic velocity. In the drift band, however, a revision of the theory is required. In this regime of velocity, the magnetic island radiates drift waves which can affect the dynamics of the system. Our results show that the penetration of the magnetic field occurs more easily than predicted by the theoretical models, which commonly neglect drift wave radiation effects.