In a previous work, we reported on the discovery of supersonic magnetic upflows on granular cells in data from the SUNRISE/IMaX instrument. In the present work, we investigate the physical origin of these events employing data from the same instrument but with higher spectral sampling. By means of the inversion of Stokes profiles we are able to recover the physical parameters (temperature, magnetic field, line-of-sight velocity, etc.) present in the solar photosphere at the time of these events. The inversion is performed in a Monte-Carlo-like fashion, that is, repeating it many times with different initializations and retaining only the best result. We find that many of the events are characterized by a reversal in the polarity of the magnetic field along the vertical direction in the photosphere, accompanied by an enhancement in the temperature and by supersonic line-of-sight velocities. In about half of the studied events, large blueshifted and redshifted line-of-sight velocities coexist above/below each other. These features can be explained in terms of magnetic reconnection, where the energy stored in the magnetic field is released in the form of kinetic and thermal energy when magnetic field lines of opposite polarities coalesce. However, the agreement with magnetic reconnection is not perfect and, therefore, other possible physical mechanisms might also play a role.