Reconfigurable intelligent surface (RIS) has been identified as a promising technology for future wireless communication systems due to its ability to manipulate the propagation environment intelligently. RIS is a frequency-selective device, thus it can only effectively manipulate the propagation of signals within a specific frequency band. This frequency selective characteristic can make deploying RIS in wireless cellular networks more challenging, as adjacent base stations (BSs) operate on different frequency bands. In addition, rate-splitting multiple access (RSMA) scheme has been shown to enhance the performance of RIS-aided multi-user communication systems. Accordingly, this work considers a more practical reflection model for RIS-aided RSMA communication systems, which accounts for the responses of signals across different frequency bands. To that end, new analytical expressions for the ergodic sum-rate are derived using the moment generating function (MGF) and Jensen inequality. Based on these analytical sum-rate expressions, novel practical RIS reflection designs and power allocation strategies for the RSMA scheme are proposed and investigated to maximize the achievable sum-rate in RIS-assisted multi-cell, multi-band cellular networks. Simple sub-optimal designs are also introduced and discussed. The results validate the significant gains of our proposed reflection design algorithms with RSMA over conventional schemes in terms of achievable sum-rate. Additionally, the power allocation strategy for the RSMA scheme is shown to offer superior performance compared to conventional precoding schemes that do not rely on RSMA.