Real-world image search queries are multimodal and compositional: ``find this shirt in pink'' specifies an entity to retain, an attribute to modify, and context to ignore. Yet existing re-rankers either compress such multifaceted relevance into an opaque embedding or rely on free-form chain-of-thought that easily omits or hallucinates fine-grained constraints. Drawing on rubric- and checklist-based evaluation from NLP, we recast multimodal image re-ranking as a semantic constraint satisfaction problem and propose EviRank, which parses any query - text-only, image-only, or composed - into a unified evidence package: typed criteria across six semantic slots (e.g., entities, attributes, relations), each labelled required, forbidden, or ignorable. Re-ranking then reduces to evidence-conditioned verification, combining deterministic rubric scoring and evidence-grounded listwise comparison in a single training-free procedure. The explicit evidence can further serve as structured supervision for optionally distilling a lightweight student. Across five benchmarks spanning text-to-image, image-to-image, and composed image retrieval, EviRank achieves state-of-the-art performance, and the distilled student preserves over 90% of the teacher's capability at substantially lower cost.