Humanoid robots have recently achieved remarkable success in motion tracking. However, during real-world deployment, robots inevitably encounter dynamics gaps arising from either extra physical disturbances or inaccurate simulation modeling, resulting in a significant training-deployment gap. Therefore, effectively leveraging real-world data to fine-tune policies represents the crucial last mile for robust deployment. To bridge this gap, we propose HumanoidNDM, an online fine-tuning framework for humanoid motion tracking driven by a real-world-trained neural dynamics model. First, in the data collection stage, we introduce a low-frequency reference perturbation method with an adaptive intensity mechanism, balancing deployment feasibility and exploration efficiency. Second, for the model training stage, we train a robust history-based, proprioceptive neural dynamics model in Euclidean space by incorporating differentiable forward kinematics, eliminating the reliance on costly motion capture systems. Finally, in the policy fine-tuning stage, we directly fine-tune the policy via backpropagated model gradients, achieving high data efficiency. Through physical validation on the Unitree G1 robot, we demonstrate that HumanoidNDM enables rapid real-world adaptation to various perturbations, representing the first online, MoCap-free fine-tuning framework for humanoid tracking policies.