Recently developed optimally tuned range-separated hybrid (OT-RHS) functionals within time-dependent density functional theory have been shown to address existing limitations in calculating charge transfer excited state energies. The RSH success in improving the calculation of CT states stems from enforcing the correspondence of the frontier molecular orbitals (FMOs) to physical properties, where the highest occupied MO energy relates to the ionization potential and the lowest unoccupied MO energy relates to the electron affinity. However, in this work, we show that a less accurate description of CT states that involves non-FMOs is afforded by the RSH approach. In order to achieve a high quality description of such higher energy CT states, the parameter tuning procedure, which lies at the foundation of the RSH approach, needs to be generalized to consider the CT process. We demonstrate the need for improved description of such CT states in donor-acceptor systems, where the optimal tuning parameter is accounting for the state itself.