通过分层干预视频证据，有效减少视频大模型的时空幻觉。

Video Large Language Models (Video-LLMs) remain prone to spatiotemporal hallucinations, often generating visually unsupported details or incorrect temporal relations. Existing mitigation methods typically treat hallucination as a uniform decoding failure, applying globally shared correction rules. We instead observe that decoder layers contribute differently to visual grounding and later linguistic composition, indicating that intervention must be layer-aware. Based on this insight, we propose STEAR, a layer-aware spatiotemporal evidence intervention framework. STEAR identifies high-risk decoding steps and selects token-conditioned visual evidence from grounding-sensitive middle layers. It uses this shared evidence for two coupled purposes: restoring missing local grounding in middle layers, and constructing temporally perturbed patch-level counterfactuals to falsify inconsistent reasoning during late-layer decoding. Consequently, STEAR mitigates both spatial and temporal hallucinations within an efficient single-encode inference framework. Experiments across representative Video-LLM backbones and challenging benchmarks demonstrate that STEAR consistently reduces hallucinations while improving faithfulness, temporal consistency, and robustness. Our results confirm that reliable video decoding relies on intervening on precise evidence at the right layer, rather than enforcing a global penalty. The code is provided in the Supplementary Material.