In the light-matter strong coupling regime, the excited state of quantum emitters is inextricably linked to a photonic mode, leading to hybrid states that are part-light and part-matter. Recently, there has been huge effort to realize strong coupling with nanoplasmonics, since it provides a versatile environment to study and control molecules in ambient conditions. Amongst the most promising designs are plasmonic nano-cavities that confine light to unprecedentedly small volumes. Such nano-cavities though support multiple types of modes, with different field profiles and radiative decay rates (bright and dark modes). Here, we show theoretically that the different nature of these modes leads to mode beating within the nano-cavity and the Rabi-oscillations, which alters the spatio-temporal dynamics of the hybrid system. By specifically designing the illumination set-up, we decompose and control the dark and bright plasmon mode excitation and therefore their coupling with quantum emitters. Hence, this work opens new routes for dynamically dressing emitters, to tailor their hybrid states with external radiation.