Social media data has been used for detecting users with mental disorders, such as depression. Despite the global significance of cross-cultural representation and its potential impact on model performance, publicly available datasets often lack crucial metadata relatedto this aspect. In this work, we evaluate the generalization of benchmark datasets to build AI models on cross-cultural Twitter data. We gather a custom geo-located Twitter dataset of depressed users from seven countries as a test dataset. Our results show that depressiondetection models do not generalize globally. The models perform worse on Global South users compared to Global North. Pre-trainedlanguage models achieve the best generalization compared to Logistic Regression, though still show significant gaps in performance on depressed and non-Western users. We quantify our findings and provide several actionable suggestions to mitigate this issue