We present numerical and experimental investigations of the synchronization of the coupling-induced instabilities in two distant mutually-coupled semiconductor lasers. In our experiments, two similar Fabry-Perot lasers are coupled via their coherent optical fields. Our theoretical framework is based on a rate equation model obtained under weak coupling conditions. In both experiments and simulations, we find (achronal) synchronization of sub-nanosecond intensity fluctuations in concurrence with an asymmetric physical role among the lasers, even under symmetric operating conditions. We explore the synchronization of these instabilities with respect to the coupling strength and the injection current. We demonstrate the existence of a critical coupling strength, below which synchronization is lost, however dynamical instabilities persist. Our model correctly reproduces the observed dynamical features over the entire investigated parameter space. We provide an intuitive explanation of the appearance of the achronal solution by analyzing the dynamics of the injection phases of the optical fields.