Unmanned Aerial Vehicles (UAVs) are integral in various sectors like agriculture, surveillance, and logistics, driven by advancements in 5G. However, existing research lacks a comprehensive approach addressing both data freshness and security concerns. In this paper, we address the intricate challenges of data freshness, and security, especially in the context of eavesdropping and jamming in modern UAV networks. Our framework incorporates exponential AoI metrics and emphasizes secrecy rate to tackle eavesdropping and jamming threats. We introduce a transformer-enhanced Deep Reinforcement Learning (DRL) approach to optimize task offloading processes. Comparative analysis with existing algorithms showcases the superiority of our scheme, indicating its promising advancements in UAV network management.