Does it do it when the cable is plugged in by itself, or only if the audio source is also plugged into the other end of the cable?
PTT is done by grounding the tip to the shield/ground on an aviation mic jack. Current flows from the radio and/or intercom to the normally open PTT switch(es), and when the voltage on the tip is grounded, the radio keys and switches from receive to transmit.
If the radio keys as soon as you plug *only* the cable in with nothing else attached to the cable, it's likely that the plug doesn't fit the jack correctly and tip is being shorted to ground right inside the aircraft's jack, but there's also a possibility that something screwy is going on inside the cable. Using an ohmmeter, you can test the cable when disconnected from everything and see if the tip is connected to anything. It should not be.
If the radio only keys once the audio source is plugged into the cable, the audio device is allowing current to flow between the tip and sleeve of the aircraft end of the cable, which are probably hooked to the tip and ring on the other end of the cable at the audio device.
If the latter, you may need a capacitor in-line to block the DC trying to flow, or a 1:1 audio transformer for the purists...
(The blocking capacitor creates an RC filter circuit with any upstream resistance in the cable, and can alter the quality of the audio a bit), depending on the resistance and capacitance values... not that it's going to matter much in a noisy aircraft.)
The other problem and also a likely culprit -- on the audio device end of the cable, you're dealing with a stereo connection where tip and ring are split into two (left and right, I forget which is which, but Google will find that), and shield which is ground.
You're taking two signals and feeding them to a mono jack. There's a few ways to handle that, but it could also be a source of where your pseudo-ground is showing up. Example, the iPod and iPhone actually use a four conductor plug, but that same jack will accept a standard 1/8" stereo jack which is only three conductor.
Your "sneak path" to ground from the aircraft tip might be something like that.
Google revealed this, which may help if you're into schematics and visuals...
http://www.aeroelectric.com/articles/micjack/micjack.html
The "extra ring" he talks about, found on many mic plugs, is called a "guard ring" and may or may not be grounded too (and/or causing your problem). I prefer the guard not to be grounded and floating instead, but have seen them both ways.