The magnetic island evolution under the action of a current generated externally by electron cyclotron wave beams is studied using a reduced resistive magnetohydrodynamics plasma model. The use of a two-dimensional reconnection model shows novel features of the actual nonlinear evolution as compared to the zero-dimensional model of the generalized Rutherford equation. When the radio frequency control is applied to a small magnetic island, the complete annihilation of the island width is followed by a spatial phase shift of the island, referred as “flip” instability. On the other hand, a current-drive injection in a large nonlinear island can be accompanied by the occurrence of a Kelvin-Helmholtz instability. These effects need to be taken into account in designing tearing mode control systems based on radio frequency current-drive.