Hand exoskeletons and functional electrical stimulation (FES) have shown promise in restoring hand function after stroke or cervical spinal cord injury. However, major challenges remain in providing reliable user command input in individuals with severe paralysis and in enabling safe and effective control of hand closing and opening. Here, we present a non-invasive tongue-based control strategy for a hybrid soft hand exoskeleton system combining tongue-controlled independent tendon-driven flexion of five fingers with tongue-triggered FES-induced finger extension. This user-intent-driven hybrid approach supports multiple activities of daily living, such as grasping a bottle or toothbrush, and enables hand opening while mitigating muscle fatigue and reducing system complexity. The system was evaluated in five users with cervical spinal cord injury, demonstrating high task success rates in daily living tasks and user preference due to its wearability and ease of use, as well as consistently low reported levels of discomfort, pain, and fatigue. These findings show that the proposed hybrid system can restore activities of daily living in individuals with cervical tetraplegia, including those with long-term injuries.