Reinforcement learning (RL) post-training substantially improves remote sensing vision-language models (RS-VLMs). However, when handling complex remote sensing imagery (RSI) requiring exhaustive visual scanning, models tend to rely on localized salient cues for rapid inference. We term this RL-induced bias "perceptual inertia". Driven by reward maximization, models favor quick outcome fitting, leading to two limitations: cognitively, overreliance on specific features impedes complete evidence construction; operationally, models struggle to flexibly shift visual focus across tasks. To address this bias and encourage comprehensive visual evidence mining, we propose RS-HyRe-R1, a hybrid reward framework for RSI understanding. It introduces: (1) a spatial reasoning activation reward that enforces structured visual reasoning; (2) a perception correctness reward that provides adaptive quality anchors across RS tasks, ensuring accurate geometric and semantic alignment; and (3) a visual-semantic path evolution reward that penalizes repetitive reasoning and promotes exploration of complementary cues to build richer evidence chains. Experiments show RS-HyRe-R1 effectively mitigates "perceptual inertia", encouraging deeper, more diverse reasoning. With only 3B parameters, it achieves state-of-the-art performance on REC, OVD, and VQA tasks, outperforming models up to 7B parameters. It also demonstrates strong zero-shot generalization, surpassing the second-best model by 3.16%, 3.97%, and 2.72% on VQA, OVD, and REC, respectively. Code and datasets are available at https://github.com/geox-lab/RS-HyRe-R1.