The sedimentation of an initially inhomogeneous distribution of hard-sphere colloids confined in a slit is simulated using the multi-particle collision dynamics scheme which takes into account hydrodynamic interactions mediated by the solvent. This system is an example for soft matter driven out of equilibrium where various length and time scales are involved. The initial laterally homogeneous density profiles exhibit a hydrodynamic Rayleigh-Taylor-like instability. Solvent backflow effects lead to an intricate non-linear behaviour which is analyzed via the solvent flow field and the colloidal velocity correlation function. Our simulation data are in good agreement with real-space microscopy experiments.