Enhancing the accuracy and efficiency of machine learning algorithms employed in neural interface systems is crucial for advancing next-generation intelligent therapeutic devices. However, current systems often utilize basic machine learning models that do not fully exploit the natural structure of brain signals. Additionally, existing learning models used for neural signal processing often demonstrate low speed and efficiency during inference. To address these challenges, this study introduces Micro Tree-based NAM (MT-NAM), a distilled model based on the recently proposed Neural Additive Models (NAM). The MT-NAM achieves a remarkable 100$\times$ improvement in inference speed compared to standard NAM, without compromising accuracy. We evaluate our approach on the CHB-MIT scalp EEG dataset, which includes recordings from 24 patients with varying numbers of sessions and seizures. NAM achieves an 85.3\% window-based sensitivity and 95\% specificity. Interestingly, our proposed MT-NAM shows only a 2\% reduction in sensitivity compared to the original NAM. To regain this sensitivity, we utilize a test-time template adjuster (T3A) as an update mechanism, enabling our model to achieve higher sensitivity during test time by accommodating transient shifts in neural signals. With this online update approach, MT-NAM achieves the same sensitivity as the standard NAM while achieving approximately 50$\times$ acceleration in inference speed.