There are two common uses for the RTS and CTS flow control signals. The first provides a full handshake with the two signals such that the DTE sends RTS requesting to send data, and DCE responds with CTS signaling it is ready and is excepting to receive data.
However the alternative definition defined in the latest version of TIA/EIA-232 has been in popular use for quite a while. In this definition each device uses its output independently to let the other device know when it is okay to send data.
CTS still indicates whether the DCE is ready to receive data or not. But now RTS is redefined as the DTE's Ready for receiving. Each device checks the opposite ends's signal before transmitting.
This second definition is what is implemented in the USB to Serial reference design. This allows proper flow control signaling for both a DTE to DCE system, or a DTE to DTE system (with Null Modem).