In129 Xe+ nat Sn central collisions from 8 to 25 MeV/A, the three-fragment exit channel occurs with a significant cross section. We show that these fragments arise from two successive binary splittings of a heavy composite system. The sequence of fragment production is determined. Strong Coulomb proximity effects are observed in the three-fragment final state. A comparison with Coulomb trajectory calculations shows that the time scale between the consecutive break-ups decreases with increasing bombarding energy, becoming quasi-simultaneous above excitation energy E * = 4.0±0.5 MeV/A. This transition from sequential to simultaneous break-up was interpreted as the signature of the onset of multifragmentation for the three-fragment exit channel in this system.