Reconstruction-based frameworks are widely adopted in Time Series Anomaly Detection (TSAD), assuming that models reconstruct normal behavior well but yield larger errors on anomalies. However, in unsupervised TSAD, minimizing reconstruction loss alone often breaks this assumption. Models tend to overfit local patterns for trivial reconstruction and fail to capture the global dependencies that characterize normal behavior. Consequently, anomalies that violate global dependencies can also be reconstructed well, leading to a misalignment between reconstruction and detection. To address this challenge, we propose AnoMamba, a novel TSAD framework that aligns reconstruction with anomaly detection by enhancing global dependency modeling. Specifically, AnoMamba employs patch embedding to reduce local redundancy and introduces a Mamba variant with global step-size reweighting to select meaningful global dependencies. The reweighting process is guided by multi-scale long-tail priors, which adaptively balance global and local dependencies to mitigate overfitting in the unsupervised setting. Extensive experiments on both univariate and multivariate benchmarks demonstrate that AnoMamba consistently outperforms state-of-the-art methods in both accuracy and efficiency, while offering interpretability through its hidden attention map.