We demonstrate that the transient non-autonomous dynamics of a spin torque nano-oscillator (STNO) under a radio-frequency (rf) driving signal is qualitatively different from the dynamics described by the Adler model. If the external rf current \(I_{rf}\) is larger than a certain critical value \(I_{cr}\) (determined by the STNO bias current and damping) strong oscillations of the STNO power and phase develop in the transient regime. The frequency of these oscillations increases with \(I_{rf}\) as \(\propto\sqrt{I_{rf} - I_{cr}}\) and can reach several GHz, whereas the damping rate of the oscillations is almost independent of \(I_{rf}\). This oscillatory transient dynamics is caused by the strong STNO nonlinearity and should be taken into account in most STNO rf applications.