Unified video models exhibit strong capabilities in understanding and generation, yet they struggle with reason-informed visual editing even when equipped with powerful internal vision-language models (VLMs). We attribute this gap to two factors: (1) existing datasets are inadequate for training and evaluating reasoning-aware video editing, and (2) an inherent disconnect between the models' reasoning and editing capabilities, which prevents understanding from guiding the editing process. To address this, we introduce the Reason-Informed Video Editing (RVE) task, which requires reasoning about physical plausibility and causal dynamics during editing. To support systematic evaluation, we construct RVE-Bench, a comprehensive benchmark with two complementary subsets: Reasoning-Aware Video Editing (RAVE) and In-Context Video-to-Video Generation (ICVG), spanning diverse reasoning dimensions across both editing and generation scenarios. Building upon this foundation, we propose ReViSE, a self-reflective learning framework that harnesses the model's internal VLM to evaluate and refine its own generation during training. Unlike prior reward-based approaches that rely on external critics, ReViSE leverages the model's internal VLM as a self-reflective evaluator, providing differentiable feedback that directly refines the generator's reasoning behavior during training. Extensive experiments on RVE-Bench demonstrate that ReViSE enhances editing accuracy and visual fidelity, outperforming the finetuned counterpart by 10% in Overall score on the RAVE subset, demonstrating the effectiveness of self-reflective differentiable reward.