Pretrained vision-language models (VLMs) such as CLIP excel in general multimodal comprehension but often struggle to capture nuanced, context-dependent visual cues. This makes it difficult to distinguish between similar-looking concepts with potentially different cultural meanings. Such deficiencies are mainly due to a limited amount of high-quality cultural data, contextual information, and the lack of negative examples that highlight subtle differences. To mitigate this, we design a data curation pipeline leveraging open-sourced VLMs and text-to-image models to construct CulTwin, a synthetic cultural dataset. This dataset consists of paired concept-caption-image triplets, where concepts visually resemble each other but are culturally different. Then, we fine-tune CLIP on CulTwin to develop CultureCLIP, which aligns cultural concepts with contextually enhanced captions and synthetic images through tailored contrastive learning. Experiments on culture-specific benchmarks show that CultureCLIP outperforms the base CLIP, achieving up to a notable 5.49% improvement in fine-grained concept recognition on certain tasks while preserving CLIP's original generalization ability, validating the effectiveness of our data synthesis and VLM backbone training paradigm in capturing subtle cultural distinctions.