We study the dynamics of the deformation of a soft liquid-liquid interface by the optical radiation pressure of a focused cw Gaussian laser beam. We measured the temporal evolution of both the hump height and the hump curvature by direct observation and by detecting the focusing effect of the hump acting as a lens. Extending the results of Yoshitake [J. Appl. Phys. 97, 024901 (2005)] to the case of liquid-liquid interfaces and to the Bo approximately =1 regime [Bo=(omega0/lc)2, , where omega0 is the beam waist and lc the capillary length], we show that, in the Bo<<1 and Bo approximately =1 ranges, the small-amplitude deformations are correctly described by a linear hydrodynamic theory predicting an overdamped dynamics. We also study the dynamics of the large-amplitude interface deformations at the onset of optohydrodynamic instability [Phys. Rev. Lett. 90, 144503 (2003)]. Using a simple, phenomenological model for the nonlinear evolution of the hump height, we interpret the observed interface dynamics at the instability onset as the signature of an imperfect subcritical instability.