In this letter, we design a downlink multi-user communication framework based on Rate-Splitting Multiple Access (RSMA) for semantic-aware networks. First, we formulate an optimization problem to obtain the optimal user scheduling, precoding, and power allocation schemes jointly. We consider the metric Age of Incorrect Information (AoII) in the objective function of the formulated problem to maximize the freshness of the overall information to be transmitted. Using big-M and Successive Convex Approximation (SCA) methods, we convert the resulting non-convex problem with conditional objective and constraints into a convex one and propose an iterative algorithm to solve it. By numerical results, we show that RSMA achieves a lower AoII than SDMA owing to its superior performance under multi-user interference.