Real-time human-device interaction in industrial Metaverse faces challenges such as high computational load, limited bandwidth, and strict latency. This paper proposes a task-oriented edge-assisted cross-system framework using digital twins (DTs) to enable responsive interactions. By predicting operator motions, the system supports: 1) proactive Metaverse rendering for visual feedback, and 2) preemptive control of remote devices. The DTs are decoupled into two virtual functions-visual display and robotic control-optimizing both performance and adaptability. To enhance generalizability, we introduce the Human-In-The-Loop Model-Agnostic Meta-Learning (HITL-MAML) algorithm, which dynamically adjusts prediction horizons. Evaluation on two tasks demonstrates the framework's effectiveness: in a Trajectory-Based Drawing Control task, it reduces weighted RMSE from 0.0712 m to 0.0101 m; in a real-time 3D scene representation task for nuclear decommissioning, it achieves a PSNR of 22.11, SSIM of 0.8729, and LPIPS of 0.1298. These results show the framework's capability to ensure spatial precision and visual fidelity in real-time, high-risk industrial environments.