Multi-video event understanding demands models that can locate and attribute query-relevant evidence scattered across long, heterogeneous video corpora. Existing large vision-language models (LVLMs) often underperform in this regime because they quickly exhaust their context budget and struggle to precisely localize evidentially important segments, frequently missing dense informational cues such as broadcast graphics, subtitles, and scoreboards. We introduce TRACE, an evidence grounding-guided framework that follows a ground-before-reasoning strategy for multi-video event reasoning. Our approach first builds a structured, text-searchable timeline for each video using OCR and object detection. A text-only LLM then conducts query-aware evidence localization, selecting relevant moments prior to any downstream visual reasoning. The retrieved frames and their grounding summaries are subsequently used to steer LVLM-based claim generation and cross-video citation consolidation. Experiments on MAGMaR 2026 and WikiVideo demonstrate that structured grounding markedly boosts factual completeness and attribution fidelity. On the MAGMaR validation split, TRACE raises macro-average MiRAGE F1 from 0.705 to 0.811 compared to an unguided Qwen3-VL-30B baseline, with especially strong improvements in citation recall from 0.440 to 0.628. The method also attains state-of-the-art results on the official MAGMaR 2026 leaderboard. Code is released at https://github.com/pengyu965/TRACE.