Nano-contact spin-torque vortex oscillators (STVOs) are anticipated to find application as nanoscale sources of microwave emission in future technological applications. Presently the output power and phase stability of individual STVOs are not competitive with existing oscillator technologies. Synchronisation of multiple nano-contact STVOs via magnetisation dynamics has been proposed to enhance the microwave emission. The control of device-to-device variations, such as mode splitting of the microwave emission, is essential if multiple STVOs are to be successfully synchronised. In this work a combination of electrical measurements and time-resolved scanning Kerr microscopy (TRSKM) was used to demonstrate how mode splitting in the microwave emission of STVOs was related to the magnetisation dynamics that are generated. The free-running STVO response to a DC current only was used to identify devices and bias magnetic field configurations for which single and multiple modes of microwave emission were observed. Stroboscopic Kerr images were acquired by injecting a small amplitude RF current to phase lock the free-running STVO response. The images showed that the magnetisation dynamics of a multimode device with moderate splitting could be controlled by the injected RF current so that they exhibit similar spatial character to that of a single mode. Significant splitting was found to result from a complicated equilibrium magnetic state that was observed in Kerr images as irregular spatial characteristics of the magnetisation dynamics. Such dynamics were observed far from the nano-contact and so their presence cannot be detected in electrical measurements. This work demonstrates that TRSKM is a powerful tool for the direct observation of the magnetisation dynamics generated by STVOs that exhibit complicated microwave emission. Characterisation of such dynamics outside the nano-contact perimeter permits a deeper insight into the requirements for optimal phase-locking of multiple STVOs that share common magnetic layers.