The photon/electron-stimulated desorption dynamics of ammonia from the Cu(111) and Cu(100) surfaces is investigated using a three-dimensional two-state quantum model, which includes the desorption and ammonia inversion coordinates as well as the "spinning" rotational degree of freedom. The desorption dynamics is followed by time-dependent wave packet on the ground or excited electronic state. Rotational state populations of both NH3 and ND3, obtained from the asymptotic wave packet, can be approximated by Boltzmann distributions and they show strong dependence on the symmetry and corrugation of the Cu surface. The NH3 rotational temperature of T-rot=205 K on Cu(111) and 372 K on Cu(100) agree well with experimental observations. The desorbed NH3 is found to be rotational hotter than ND3, also in agreement with experiment. The addition of the rotational degree of freedom has little impact on other aspects of the dynamics, including desorption yield and vibrational excitation.