As mobile robots increasingly operate alongside humans in shared workspaces, ensuring safe, efficient, and interpretable Human-Robot Interaction (HRI) has become a pressing challenge. While substantial progress has been devoted to human behavior prediction, limited attention has been paid to how humans perceive, interpret, and trust robots' inferences and how robots plan safe and efficient trajectories based on predicted human behaviors. To address these challenges, this paper presents XR-DT, an eXtended Reality-enhanced Digital Twin framework for mobile robots, which bridges physical and virtual spaces to enable bi-directional understanding between humans and robots. Our hierarchical XR-DT architecture integrates augmented-, virtual-, and mixed-reality layers, fusing real-time sensor data, simulated environments in the Unity game engine, and human feedback captured through wearable XR devices. Within this framework, we design a novel Human-Aware Model Predictive Path Integral (HA-MPPI) control model, an MPPI-based motion planner that incorporates ATLAS (Attention-based Trajectory Learning with Anticipatory Sensing), a multi-modal Transformer model designed for egocentric human trajectory prediction via XR headsets. Extensive real-world experimental results demonstrate accurate human trajectory prediction, and safe and efficient robot navigation, validating the HA-MPPI's effectiveness within the XR-DT framework. By embedding human behavior, environmental dynamics, and robot navigation into the XR-DT framework, our system enables interpretable, trustworthy, and adaptive HRI.