Knowledge Editing (KE) has emerged as a promising paradigm for updating facts in Large Language Models (LLMs) without retraining. However, progress in Multilingual Knowledge Editing (MKE) is currently hindered by biased evaluation frameworks. We observe that existing MKE benchmarks are typically constructed by mechanically translating English-centric datasets into target languages (e.g., English-to-Chinese). This approach introduces translation artifacts and neglects culturally specific entities native to the target language, failing to reflect the true knowledge distribution of LLMs. To address this, we propose CLM-Bench, a culture-aware benchmark constructed using a native Chinese-first methodology. We curate 1,010 high-quality CounterFact pairs rooted in Chinese cultural contexts and align them with English counterparts. Using CLM-Bench, we conduct extensive experiments on representative LLMs (e.g., Llama-3, Qwen2) and reveal a significant Cross-lingual Misalignment: edits in one language function independently and fail to propagate to the other. We further provide a geometric explanation via layer-wise representation analysis, demonstrating that edit vectors for Chinese and English are nearly orthogonal -- residing in disjoint subspaces -- while mixed-lingual editing exhibits linear additivity of these vectors. Our findings challenge the effectiveness of current methods in cross-lingual transfer and underscore the importance of culturally native benchmarks.