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Most automated peer review systems rely on textual manuscript content alone, leaving visual elements such as figures and external scholarly signals underutilized. We introduce REM-CTX, a reinforcement-learning system that incorporates auxiliary context into the review generation process via correspondence-aware reward functions. REM-CTX trains an 8B-parameter language model with Group Relative Policy Optimization (GRPO) and combines a multi-aspect quality reward with two correspondence rewards that explicitly encourage alignment with auxiliary context. Experiments on manuscripts across Computer, Biological, and Physical Sciences show that REM-CTX achieves the highest overall review quality among six baselines, outperforming other systems with substantially larger commercial models, and surpassing the next-best RL baseline across both quality and contextual grounding metrics. Ablation studies confirm that the two correspondence rewards are complementary: each selectively improves its targeted correspondence reward while preserving all quality dimensions, and the full model outperforms all partial variants. Analysis of training dynamics reveals that the criticism aspect is negatively correlated with other metrics during training, suggesting that future studies should group multi-dimension rewards for review generation.