In order to make future wireless communication networks efficient in spectrum and energy, reconfigurable intelligent surface (RIS) has become a practical technology that can significantly improve the coverage and performance of wireless networks. In this paper, we discuss the application of RIS technology in Rate-Splitting Multiple Access (RSMA), where the base station (BS) sends superimposed signals to multiusers through RIS. To delve deeper into investigating the efficacy of RIS-aided RSMA networks, we adopt a On-Off control scheme and consider the system performance under imperfect successive interference cancellation (ipSIC) and perfect successive interference cancellation (pSIC) respectively. On this basis, we use ipSIC/pSIC to derive the outage probability expression of the kth user. Based on the outcome analysis, the diversity order of users exhibits a correlation with the quantity of reflective elements in the RIS and channel prioritization under pSIC conditions. In addition, increasing the quantity of RIS reflective units can make up for the decrease of system outage performance caused by residual interference, and further improve the outage performance of the system.