Single-mode frequency-tuneable semiconductor lasers based on monolithic integration of multiple cavity sections are important components, widely used in optical communications, photonic integrated circuits and other optical technologies. To date, investigations of the ultrafast switching processes in such lasers, essential to reduce frequency cross-talk, have been restricted to the observation of intensity switching over nanosecond-timescales. Here, we report coherent measurements of the ultrafast switch-on dynamics, mode competition and frequency selection in a monolithic frequency-tuneable laser using coherent time-domain sampling of the laser emission. This approach allows us to observe hopping between lasing modes on picosecond-timescales and the temporal evolution of transient multi-mode emission into steady-state single mode emission. The underlying physics is explained through a full multi-mode, temperature-dependent carrier and photon transport model. Our results show that the fundamental limit on the timescales of frequency-switching between competing modes varies with the underlying Vernier alignment of the laser cavity.