Event cameras generate asynchronous signals in response to pixel-level brightness changes, offering a sensing paradigm with theoretically microsecond-scale latency that can significantly enhance the performance of multi-sensor systems. Extrinsic calibration is a critical prerequisite for effective sensor fusion; however, the configuration that involves event cameras remains an understudied topic. In this paper, we propose a motion-based temporal and rotational calibration framework tailored for event-centric multi-sensor systems, eliminating the need for dedicated calibration targets. Our method uses as input the rotational motion estimates obtained from event cameras and other heterogeneous sensors, respectively. Different from conventional approaches that rely on event-to-frame conversion, our method efficiently estimates angular velocity from normal flow observations, which are derived from the spatio-temporal profile of event data. The overall calibration pipeline adopts a two-step approach: it first initializes the temporal offset and rotational extrinsics by exploiting kinematic correlations in the spirit of Canonical Correlation Analysis (CCA), and then refines both temporal and rotational parameters through a joint non-linear optimization using a continuous-time parametrization in SO(3). Extensive evaluations on both publicly available and self-collected datasets validate that the proposed method achieves calibration accuracy comparable to target-based methods, while exhibiting superior stability over purely CCA-based methods, and highlighting its precision, robustness and flexibility. To facilitate future research, our implementation will be made open-source. Code: https://github.com/NAIL-HNU/EvMultiCalib.