The reconfigurable intelligent surface (RIS) aided index modulation (IM) is a promising technology for next-generation wireless communications. However, acquiring channel state information (CSI) for RIS-based IM requires expensive pilot overhead, especially for the IM in multiple domains. In this paper, a novel rectangular differential reflecting spatial modulation (RDRSM) system is proposed for the RIS-aided multiple-input multiple-output (MIMO) system. Specifically, the proposed multi-antenna-activated RDRSM (M-RDRSM) scheme utilizes a rectangular dispersion matrix (DM) to jointly map a digital beamforming (DBF) weight vector and a RIS reflection pattern to perform the rectangular differential modulation. A thorough analysis presents that the proposed M-RDRSM scheme can achieve high-spectral efficiency, low complexity of the system, and noncoherent decoding without prior knowledge of CSI in the space-reflection dual-domain IM. Further, the proposed M-RDRSM scheme is simplified to a single-antenna-activated RDRSM (S-RDRSM) scheme, which can reduce the hardware cost and avoid the inter-antenna synchronization problem more effectively. Simulation results demonstrate that the proposed RDRSM scheme performs better in terms of bit error rate performance and achieve a lower decoding complexity than the existing correlated differential IM schemes with the same achievable spectral efficiency.