Multimodal pre-trained models (e.g., ImageBind), which align distinct data modalities into a shared embedding space, have shown remarkable success across downstream tasks. However, their increasing adoption raises serious security concerns, especially regarding targeted adversarial attacks. In this paper, we show that existing targeted adversarial attacks on multimodal pre-trained models still have limitations in two aspects: generalizability and undetectability. Specifically, the crafted targeted adversarial examples (AEs) exhibit limited generalization to partially known or semantically similar targets in cross-modal alignment tasks (i.e., limited generalizability) and can be easily detected by simple anomaly detection methods (i.e., limited undetectability). To address these limitations, we propose a novel method called Proxy Targeted Attack (PTA), which leverages multiple source-modal and target-modal proxies to optimize targeted AEs, ensuring they remain evasive to defenses while aligning with multiple potential targets. We also provide theoretical analyses to highlight the relationship between generalizability and undetectability and to ensure optimal generalizability while meeting the specified requirements for undetectability. Furthermore, experimental results demonstrate that our PTA can achieve a high success rate across various related targets and remain undetectable against multiple anomaly detection methods.