Anomaly detection on temporal dynamic graphs enables the identification of threats in our cyberspaces. However, finding a graph representation that offers the best trade-off between execution time and accuracy remains a major challenge. To address this, we propose a novel model based on Hyperbolic Graph Neural Networks, an emerging class of learning architectures that leverages the expressive power of hyperbolic geometry to process graph-structured data. Our results show that the proposed model outperforms the state of the art, achieving over 97% accuracy across all datasets while also reducing memory consumption. Moreover, its processing time is competitive with the best-performing Euclidean models.