We employed time-and space-resolved full-field magnetic transmission soft x-ray microscopy to observe vortex-core gyrations in a pair of dipolar-coupled vortex-state Permalloy (Ni80Fe20) disks. The 70 ps temporal and 20 nm spatial resolution of the microscope enabled us to simultaneously measure vortex gyrations in both disks and to resolve the phases and amplitudes of both vortex-core positions. We observed their correlation for a specific vortex-state configuration. This work provides a robust and direct method of studying vortex gyrations in dipolar-coupled vortex oscillators.