We thoroughly investigate the outage performance of reconfigurable intelligent surface (RIS) aided multi-input multi-output (MIMO) communications by exploiting statistical channel state information (CSI). Kornecker channel model is adopted to characterize the impact of spatial correlations among MIMO antennas and reconfigurable reflectors. Mellin transform and random matrix theory are then utilized to derive the outage probability, with which we further conduct the asymptotic outage analysis to obtain insightful findings. In particular, the asymptotic analysis reveals that the number of reflecting elements at the RIS should not be smaller than the total number of MIMO transmit and receive antennas to get rid of the rank deficiency of the cascaded MIMO channels. Moreover, the asymptotic outage probability is a monotonically increasing and convex function with respect to the transmission rate. The numerical outcomes not only corroborate our analytical results, but also demonstrate the negative impact of the spatial correlation and the benefit of increasing the number of reconfigurable reflectors. Finally, we apply the asymptotic results to optimally devise the phase shifts with a low computational complexity.