API mode is a bridge between transparent mode and command mode. Instead of using +++ to enter command mode, issue an AT command and exit command mode, you use API Data frames using Hex characters that tell the radio what to do. If you look in your XCTU's terminal console, you will find an API frame explorer that will help you assemble the packets and send them. As a hint, if you want to send data to a specific module, you use the TX Request frame.
Something you might want to do, is to leave the PC Side in transparent mode, then put the Micro Processor side in API mode. This way the processor can know who is sending the data and on the PC side, you only need to know what data to send just like you did in transparent mode.