Official comment

Hey Rob,
The mixer should have the channel inputs set to the PC position.
Also check that your DJM-S3 Setting Utility has the audio outputs set to CONTROL TONE (PHONO):
Mine is greyed-out because it's not connected and Serato is not open.
If you're using a Mac, make sure you've allowed the audio input through security by going to System Preferences > Security & Privacy > Privacy > Microphone (left) > Serato DJ Pro (right) and check the box beside it.