We focus on the secure performance metrics at the legitimate users, i.e. secure outage probability (SOP) and secrecy capacity, to quantify the secrecy performance of NOMA-RIS-aided IoT systems. We assume the RIS is placed between the access point and the legitimate devices, and is expected to enhance the link security through the smart phase shift mechanism of metasurface elements in RIS. We first present analytical results for the SOP and secrecy capacity. Next, an iterative search algorithm is adopted to exhibit optimal SOP for further insights and analysis. In order to help the base station allocate power coefficients to NOMA users properly, an efficient deep-neural network (DNN)-based secure metric prediction scheme is adopted to achieve the secure performance. Our derivations and simulations indicate that the number of meta-surface elements of the RIS and the average signal-to-noise ratio at the base station contribute the most to the system performance enhancement.