Recent large reasoning models produce explicit reasoning traces before final answers, yet their behavior in culturally grounded reasoning remains insufficiently understood. In this work, we identify cultural overriding, a step-level failure mode in which a model initially recognizes a relevant local cultural norm but later weakens or replaces it with a more general normative frame, resulting in an incorrect judgment. To address this failure, we introduce CulturePRM, a 1B-parameter process reward model trained on step-annotated synthetic cultural reasoning traces to verify whether intermediate steps preserve, override, or are unrelated to the target cultural norm. At inference time, CulturePRM aggregates step-level rewards to rerank candidate reasoning traces via Best-of-N selection.

We evaluated CulturePRM across multiple cultural reasoning benchmarks and base reasoning models and observed consistent improvements, with gains of up to 12.06 pp. These gains were not uniform across classes and were concentrated in lower-recall classes, while performance in already strong classes was largely preserved, thereby reducing class-wise disparities. A finer-grained error analysis further revealed substantial recovery among baseline errors alongside a marked reduction in cultural overriding. These findings suggest that culturally aligned reasoning requires models not only to recognize local cultural norms, but also to preserve them throughout the reasoning process.