This paper investigates joint channel and symbol estimation in a multiple user uplink multiple-input multiple-output (MIMO) system assisted by several reconfigurable intelligent surfaces (RISs). With Khatri–Rao space–time (KRST) coding at the users, A PARATUCK2-based tensor framework is developed. To tackle the challenges of multi-RIS deployment, an adaptive accelerated fitting for PARATUCK2-based decomposition (AAF-PDE) algorithm is proposed. The algorithm employs an accelerated adaptive fitting (AAF) mechanism with dynamic step-size optimization, jointly estimating the RIS-base station (BS) channels, the composite user-RIS channels and the user symbols. Based on the accurately estimated channel matrices, geometric parameters can be further extracted via a two-dimensional ESPRIT procedure without dedicated radar signal. Simulation results verify that AAF-PDE outperforms benchmark algorithms in terms of channel estimation, symbol detection and convergence efficiency. Moreover, the root mean square error (RMSE) performance demonstrates that the geometric parameters estimation is enabled with high accuracy. Theoretical analysis on identifiability, complexity, and the Cramér–Rao bound (CRB) demonstrates the soundness of the proposed algorithm.