Source-only domain generalization (DG) for remote sensing semantic segmentation seeks reliable predictions in unseen domains without target-domain data during training. Although vision foundation models offer transferable knowledge, category recognition remains sensitive to source-specific visual cues, while task-specific adaptation may weaken pretrained transferability. We propose ASCoR, an asymmetric semantic-spatial framework built on SAM3. Its text-conditioned semantic branch uses class-name prompts to provide explicit category guidance. Probe-Once Dynamic Adaptive LoRA distributes a fixed adaptation budget across encoder blocks to limit source-specific specialization. A complementary task-specific dense branch learns multi-scale spatial representations using a separate frozen SAM3 image encoder. A lightweight reliability router integrates the two branches through bounded spatial correction based on local prediction reliability. All components are trained using source-domain supervision only. Experiments on the ISPRS, LoveDA, and OpenEarthMap benchmarks cover nine cross-domain transfers. ASCoR achieves a state-of-the-art mean IoU of 68.61% across six ISPRS transfers, outperforming the previous best method by 2.69 percentage points. It also achieves the best results on all three LoveDA/OpenEarthMap transfers, with 59.07%, 47.95%, and 49.38% mIoU on Rural-to-Urban, Urban-to-Rural, and Urban-to-OpenEarthMap, respectively. Ablation studies, feature visualizations, and spatial reliability analyses support the effectiveness and complementarity of the proposed components. Code: https://github.com/WangZitong42/ASCoR.

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