Recently, Visual State Space Models offer powerful global modeling for Dual-modal Salient Object Detection (SOD). However, they are still constrained by three inherent limitations: first, Mamba's strict reliance on sequential ordering makes it sensitive to cross-modal geometric misalignment, where spatial shifts disrupt token correspondence; second, general indiscriminate scanning treating all tokens equally may lead to signal dilution, where sparse foreground features are overwhelmed by background noise; third, conventional decoders rely on implicit upsampling, causing boundary degradation during resolution recovery. To address these challenges, we propose G-SalAlignMamba, a geometry-aware framework tailored for dual-modal SOD. We introduce Geometry-Aware Encoding with explicit alignment to correct spatial shifts, Semantics-Informed Refinement to prevent signal dilution by prioritizing foregrounds, and Structure-Preserving Decoding that integrates explicit alignment with unsupervised boundary refinement. Extensive experiments show that G-SalAlignMamba achieves state-of-the-art performance on RGB-D and RGB-T benchmarks with favorable efficiency (30.41 FPS, 83.80M parameters). The code is available at https://github.com/PC1-99/G-SalAlignMamb.git.