The growing power of generative models raises major concerns about the authenticity of published content. To address this problem, several synthetic content detection methods have been proposed for uniformly structured media such as image or text. However, little work has been done on the detection of synthetic tabular data, despite its importance in industry and government. This form of data is complex to handle due to the diversity of its structures: the number and types of the columns may vary wildly from one table to another. We tackle the tough problem of detecting synthetic tabular data ''in the wild'', i.e. when the model is deployed on table structures it has never seen before. We introduce a novel datum-wise transformer architecture and show that it outperforms existing models. Furthermore, we investigate the application of domain adaptation techniques to enhance the effectiveness of our model, thereby providing a more robust data-forgery detection solution.