I have something like this.
So I though I could use my TV as a speaker for my devices w/ a headphone jack. But when I plug all the cables in, no sound. Are the two operating on a different protocol:
The headphone jack just makes a sq. wave, sine wave etc, similar to tone() function. But RCA "protocol" doesn't work w/ that. Why not? Is there anything I can do?
You will need an adapter, amplifier.
The devise, you are trying to connect is likely produce only 1 mV of a signal (voice/audio).
Regular TV input require 775 mV.
But then how can it drive my headphones @ 1mV?
Check another thing, if maybe your TV is not blanking out as there's no video signal. My TV has a bluescreen option which I can turn off and have anything feed from its input, even if the signal is bad.
Wk
I hope you didn't pay that much. To pay $20.00 for something that costs less than $0.20 is a total rip off.
It depends where you are plugging it and what you have your TV switched to. There is no protocol involved with analogue audio only voltage levels. It is a matter of routing.
I didn't pay $20. 
Here's my pinout:
________ Red plug to tv
/
Audio out of device (headphone jack) ---- adapter<
_________ White plug to TV
And I am getting a voltage off the red+white wires, but no audio. I tried on multiple lines. Will try William's suggestion @ some point.
I think you are missing the point. Sure it goes into the sockets on the TV but where do they go? Are they inputs to the TV's audio amplifier or are they output from it. It is unusual for a TV to have audio input sockets, more likely it is an output for connecting to a hi-fi.
Suppose they are inputs, then how do you switch your TV to use them, is there an aux input or something?
It could be that if it is the TV is expecting the audio to be sitting on top of a video carrier and thus modulated at 5 or 6 MHz (depending on the TV format).
Audio wires are plugged into video 2 input. no video cable is attached.