Hybrid Reconfigurable Intelligent Surfaces (HRISs) constitute a new paradigm that redefines smart metasurfaces, not only offering tunable reflections of incoming signals, but also incorporating signal reception and processing capabilities. In this paper, leveraging the simultaneous dual-functionality of HRISs, we propose a novel framework for tracking-aided multi-user Multiple-Input Multiple-Output (MIMO) communications. In particular, a joint design of the transmit multi-user precoding matrix together with the HRIS reflection and analog combining configurations is presented, with the objective to maximize the accuracy of position estimation of multiple mobile users while meeting their individual quality-of-service constraints for sensing-aided communications. The Cramer-Rao bound for the users' positioning parameters is derived together with a prediction approach based on the extended Kalman filter. Our simulation results showcase the efficacy of the proposed Integrated Sensing And Communications (ISAC) framework over various system configuration parameters.