Deploying multi-sequence magnetic resonance imaging (MRI) segmentation models to new clinical environments is challenging due to variations in scanners and acquisition protocols. Although existing TTA methods handle basic per-modality shifts, they often fail under a fundamental dual-shift problem, as their adaptation signals fail to capture modality-interaction shifts that disrupt inter-sequence consistency. To address this, we propose Variance-gated Inter-Sequence Test-time Adaptation (VISTA), a source-free framework that tackles modality-interaction shifts. First, we design an Inter-Sequence Intervention Generator (ISIG) that generates a set of consistency probes by swapping low-frequency spectra and entropy-localized patches across sequences, preserving anatomical semantics while challenging inter-sequence dependencies. Second, we introduce Cross-View Disagreement-Aware Pseudo Labeling (CDPL), which establishes a voxel-wise reliability metric using cross-view disagreement variance to dynamically gate self-training and enforce interventional consistency, encouraging the network to rely on robust anatomical semantics. Extensive experiments adapting from standard adult MRI (BraTS-GLI-Pre) to African low-field (BraTS-SSA) and pediatric (BraTS-PED) cohorts show improved performance over competing methods under clinical shifts, achieving absolute Dice improvements of +1.89% (SSA) and +2.82% (PED) over the source model. The code is available at https://github.com/dzp2095/VISTA.

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