Rosacea is a common but underdiagnosed inflammatory skin condition that primarily affects the central face and presents with subtle redness, pustules, and visible blood vessels. Automated detection remains challenging due to the diffuse nature of symptoms, the scarcity of labeled datasets, and privacy concerns associated with using identifiable facial images. A novel privacy-preserving automated rosacea detection method inspired by clinical priors and trained entirely on synthetic data is presented in this paper. Specifically, the proposed method, which leverages the observation that rosacea manifests predominantly through central facial erythema, first constructs a fixed redness-informed mask by selecting regions with consistently high red channel intensity across facial images. The mask thus is able to focus on diagnostically relevant areas such as the cheeks, nose, and forehead and exclude identity-revealing features. Second, the ResNet-18 deep learning method, which is trained on the masked synthetic images, achieves superior performance over the full-face baselines with notable gains in terms of accuracy, recall and F1 score when evaluated using the real-world test data. The experimental results demonstrate that the synthetic data and clinical priors can jointly enable accurate and ethical dermatological AI systems, especially for privacy sensitive applications in telemedicine and large-scale screening.