Vision-language-action (VLA) models demonstrate strong generalization in robotic manipulation but face challenges in complex, real-world tasks. While supervised fine-tuning with demonstrations is constrained by data quality, reinforcement learning (RL) offers a promising alternative. We propose a human-in-the-loop dual-actor fine-tuning framework grounded in RL. The framework integrates a primary actor for robust multi-task performance with a refinement actor for latent-space adaptation. Beyond standard physical interventions, we introduce a lightweight talk-and-tweak scheme that converts human corrections into semantically grounded language commands, thereby generating a new dataset for policy learning. In real-world multi-task experiments, our approach achieves 100% success across three tasks within 101 minutes of online fine-tuning. For long-horizon tasks, it sustains a 50% success rate over 12 consecutive operations. Furthermore, the framework scales effectively to multi-robot training, achieving up to a 2 times improvement in efficiency when using dual robots. The experiment videos are available at https://sites.google.com/view/hil-daft/.