In assisted teleoperation for human-robot collaboration, accurate intention prediction is critical for enabling timely and reliable robotic assistance during long-horizon manipulation and assembly tasks. These systems require continuous understanding of user behavior to recognize actions, anticipate intentions, and detect mistakes in real time. However, robot teleoperation demonstrations are costly and hardware-limited, whereas human demonstrations are easier to collect and provide rich temporal structure. To address this challenge, we propose an uncertainty-aware human-to-robot intention prediction framework that combines: (1) hierarchical transfer learning, where MS-TCN++ is pretrained on human hand demonstrations and fine-tuned on limited robot teleoperation data to capture low-level actions and high-level task intentions; (2) a conformal prediction module that provides frame-level prediction sets with statistical coverage guarantees for reliable uncertainty quantification and early intention estimation; and (3) VLM-guided segment correction, which selectively reviews low-confidence or temporally uncertain segments using visual and temporal context. The framework supports action recognition, temporal segmentation, intention anticipation, and mistake detection for assisted teleoperation. Experiments on robot assembly demonstrations with 22 action classes show that human-to-robot fine-tuning improves the robot test-set Edit score from 70.50 to 80.70 using only 16 robot demonstrations. Edit-safe VLM correction further improves frame accuracy from 45.21% to 46.42% and increases F1@25 and F1@50 while preserving the Edit score. These results show that human demonstrations provide scalable pretraining data for robust, uncertainty-aware robot action segmentation. Code and data: project website.