In this paper, we investigate the impact of saturation nonlinear energy harvesting (EH) and activation threshold on the multiuser wireless powered sensor networks (WPSNs) from the physical layer security (PLS) perspective. In particular, for improving the secrecy performance, the generalized multiuser scheduling (GMS) scheme is exploited, in which the Kth strongest sensor is chosen based on the legitimate link. For evaluating the impact of various key parameters on the security of system, we obtain the exact closed-form expressions for secrecy outage probability (SOP) under linear EH (LEH), saturation nonlinear EH (SNEH) and saturation nonlinear EH with activation threshold (SNAT), respectively, and solve the maximization problem of secure energy efficiency (SEE). Simulation results demonstrate that: (1) the number of source sensors, the EH efficiency and the transmit power of power beacon (PB) all have positive impact on SOP, and the smaller generalized selection coefficient is advantageous for secrecy performance; (2) LEH is an ideal situation for SNEH when the saturation threshold is large enough and SNEH is a special situation for SNAT when the activation threshold is low enough; (3) the time-switching factor and the activation threshold both have an important impact on the secrecy performance, which are worth considering carefully.