Deep learning models for meteorological forecasting often fail in rare but high-impact events such as typhoons, where relevant data is scarce. Existing fine-tuning methods typically face a trade-off between overlooking these extreme events and overfitting them at the expense of overall performance. We propose TaCT, an interpretable concept-gated fine-tuning framework that solves the aforementioned issue by selective model improvement: models are adapted specifically for failure cases while preserving performance in common scenarios. To this end, TaCT automatically discovers failure-related internal concepts using Sparse Autoencoders and counterfactual analysis, and updates parameters only when the corresponding concepts are activated, rather than applying uniform adaptation. Experiments show consistent improvements in typhoon forecasting across different regions without degrading other meteorological variables. The identified concepts correspond to physically meaningful circulation patterns, revealing model biases and supporting trustworthy adaptation in scientific forecasting tasks. The code is available at https://anonymous.4open.science/r/Concept-Gated-Fine-tune-62AC.