You will have to configure the gaming headset box to use the audio coming from the c-media device for chat instead of optical or usb. Look in their tips and tricks advanced setting page for the details.
On the PS4, both directions for chat should go through the c-media.
For controlling the Push to talk, you can also add some commands to your voice file pythonw.vcl
# for in-game chat, when using the PC's audio out to send the microphone
# audio to a game console, these commands control the state of the audio
# output Mute button state (in conjunction with nircmd)
toggle mute = ShellExecute("nircmd mutesysvolume 2", 6);
mute = ShellExecute("nircmd mutesysvolume 1", 6);
mute off = ShellExecute("nircmd mutesysvolume 0", 6);
# pick one or the other of these two lines to release the mute and turn off
# the microphone until either "wake up" or a hot-key is used.
open chat = ShellExecute("nircmd mutesysvolume 0", 6) GoToSleep();
#open chat = ShellExecute("nircmd mutesysvolume 0", 6) SetMicrophone(0);
nircmd has to be installed on the path, like in the c:\windows folder so Dragon can find it.