The rapid evolution of communication technologies and the emergence of sixth-generation (6G) networks have introduced unprecedented opportunities for ultra-reliable, low-latency, and energy-efficient communication. However, the integration of advanced technologies like non-orthogonal multiple access (NOMA) and wireless powered communication networks (WPCNs) brings significant challenges, particularly in terms of energy constraints and security vulnerabilities. Traditional antenna systems and orthogonal multiple access schemes struggle to meet the increasing demands for performance and security in such environments. To address this gap, this paper investigates the impact of emerging fluid antenna systems (FAS) on the performance of physical layer security (PLS) in WPCNs. Specifically, we consider a scenario in which a transmitter, powered by a power beacon via an energy link, transmits confidential messages to legitimate FAS-aided users over information links while an external eavesdropper attempts to decode the transmitted signals. Additionally, users leverage the NOMA scheme, where the far user may also act as an internal eavesdropper. For the proposed model, we first derive the distributions of the equivalent channels at each node and subsequently obtain compact expressions for the secrecy outage probability (SOP) and average secrecy capacity (ASC), using the Gaussian quadrature methods. Our results reveal that incorporating the FAS for NOMA users, instead of the TAS, enhances the performance of the proposed secure WPCN.