We investigate the power-to-phase coupling in two commercial high bandwidth P-i-N near-IR photodetectors. We observe that a sudden change of the optical power induces a transient of the phase of the 20 GHz signal, at different time scales. The temperature rise of the photodetector junction is likely to be involved in this dynamical behaviour. The value of the bias voltage applied to the photodetector appears to control the size of the phase transients, as well as the optical power for which the slope of the amplitude-to-phase coupling cancels. These results are important in optimising RF optical links.