The formation and propagation of anti-phase boundaries (APBs) in the epitaxial growth of III-V semiconductors on Silicon is still the subject of great debate, despite the impressive number of studies focusing on this topic in the last past decades. The control of the layer phase is of major importance for the future realization of photonic integrated circuits that include efficient light sources or for new nano-electronic devices, for example. Here, it is experimentally demonstrated that the main-phase domain overgrows the anti-phase domains (APDs) because it grows faster. A large-scale analysis of the phase evolution based on reflection high-energy electron diffraction and atomic force microscopy in the case of the molecular beam epitaxy of GaSb on Silicon (001) substrate is presented. The growth rate difference between the two domains is accurately measured and is shown to come from the atomic step distribution at the III-V surface. The influence of the substrate preparation as well as of the growth condition on this distribution is also clarified.