Real-time observation of the emergence of coherent structures from noise via instabilities is of particular interest across disciplines ranging from biology to astrophysics. In the context of photonics, ultrafast fibre lasers provide an ideal test-bed for experimental observation of dynamical instabilities and generation of coherent structures of ultrashort pulses. Here we present experimentally obtained switch-on dynamics of counter-propagating ultrashort pulses in a bidirectional mode-locked fibre laser with delayed pulse formation via Q-switched and modulation instabilities, pronounced central wavelength drift, with the multiple-pulse formation. We define a localisation parameter using the round-trip resolved autocorrelation function to quantify the extent of the pulse formation, indicating an energy interchange between coherent features and background radiation. Furthermore, we report the formation of synchronised and unsynchronised dispersion waves. Our results reveal the complexity of the establishment of coherent features and their interaction with background radiation, contributing further towards the understanding of nonlinear systems in general.