Accurate and safety-conscious trajectory prediction is a key technology for intelligent transportation systems, especially in V2X-enabled urban environments with complex multi-agent interactions. In this paper, we created a digital twin-driven V2X trajectory prediction pipeline that jointly leverages cooperative perception from vehicles and infrastructure to forecast multi-agent motion at signalized intersections. The proposed model combines a Bi-LSTM-based generator with a structured training objective consisting of a standard mean squared error (MSE) loss and a novel twin loss. The twin loss encodes infrastructure constraints, collision avoidance, diversity across predicted modes, and rule-based priors derived from the digital twin. While the MSE term ensures point-wise accuracy, the twin loss penalizes traffic rule violations, predicted collisions, and mode collapse, guiding the model toward scene-consistent and safety-compliant predictions. We train and evaluate our approach on real-world V2X data sent from the intersection to the vehicle and collected in urban corridors. In addition to standard trajectory metrics (ADE, FDE), we introduce ITS-relevant safety indicators, including infrastructure and rule violation rates. Experimental results demonstrate that the proposed training scheme significantly reduces critical violations while maintaining comparable prediction accuracy and real-time performance, highlighting the potential of digital twin-driven multi-loss learning for V2X-enabled intelligent transportation systems.