While large-scale pre-training has advanced human trajectory prediction, a critical challenge remains: zero-shot transfer to unseen dataset with varying temporal dynamics. State-of-the-art pre-trained models often require fine-tuning to adapt to new datasets with different frame rates or observation horizons, limiting their scalability and practical utility. In this work, we systematically investigate this limitation and propose a robust solution. We first demonstrate that existing data-aware discrete models struggle when transferred to new scenarios with shifted temporal setups. We then isolate the temporal generalization from dataset shift, revealing that a simple, explicit conditioning mechanism for temporal metadata is a highly effective solution. Based on this insight, we present OmniTraj, a Transformer-based model pre-trained on a large-scale, heterogeneous dataset. Our experiments show that explicitly conditioning on the frame rate enables OmniTraj to achieve state-of-the-art zero-shot transfer performance, reducing prediction error by over 70\% in challenging cross-setup scenarios. After fine-tuning, OmniTraj achieves state-of-the-art results on four datasets, including NBA, JTA, WorldPose, and ETH-UCY. The code is publicly available: https://github.com/vita-epfl/omnitraj