Rate-Splitting Multiple Access (RSMA) is a robust multiple access scheme for downlink multi-antenna wireless networks. RSMA relies on multi-antenna Rate-Splitting (RS) at the transmitter and Successive Interference Cancellation (SIC) at the receivers. In this work, we study the performance of RSMA under the important setup of imperfect Channel State Information at the Transmitter (CSIT) originating from user mobility and latency/delay (between CSI acquisition and data transmission) in the network. We derive a lower bound on the ergodic sum-rate of RSMA for an arbitrary number of transmit antennas, number of users, user speed and transmit power. Then, we study the power allocation between common and private streams and obtain a closed-form solution for optimal power allocation that maximizes the obtained lower bound. The proposed power allocation greatly reduces precoder design complexity for RSMA. By Link-Level Simulations (LLS), we demonstrate that RSMA with the proposed power allocation is robust to the degrading effects of user mobility and has significantly higher performance compared to conventional multi-user (massive) Multiple-Input Multiple-Output (MIMO) strategies. The work has important practical significance as results demonstrate that, in contrast to conventional multi-user (massive) MIMO whose performance collapse under mobility, RSMA can maintain reliable multi-user connectivity in mobile deployments.