Synchronised ultrafast soliton lasers have attracted great research interest in recent decades. However, there is a lack of comprehensive understanding regarding the buildup mechanism of synchronised pulses. Here, we report a dynamic analysis of independent and synchronised solitons buildup mechanisms in synchronised ultrafast soliton lasers. The laser comprises an erbium-doped fibre cavity and a thulium-doped fibre cavity bridged with a common arm. Pulses operating at two different wavelengths formed in the cavities are synchronised by cross-phase modulation-induced soliton correlation in the common fibre arm. We find that the whole buildup process of the thulium-doped fibre laser successively undergoes five different stages: continuous wave, relaxation oscillation, quasi-mode-locking, continuous wave mode-locking and synchronised mode-locking. It is found that the starting time of the synchronised solitons is mainly determined by the meeting time of dual-color solitons. Our results will further deepen the understanding of dual-color synchronised lasers and enrich the study of complex nonlinear system dynamics.