I'll try it on my way home tonight. In the past I've noticed this problem, so I suspect it's not a problem for me now, I'm daily commuting and have been for two years straight, so I'm pretty sure mine is good ;)
Is the grip end of the cable properly secured? There should be a small metal plate that is secured by the screw that holds the throttle mechanism together. When the throttle mechanism is secured, it clamps the end of the cable to it as well.
The reason it appears when you're turning right is because it puts more bend into the cable housing and can cause it to cam out of the throttle assembly or otherwise stress it so that it pulls the cable. When turning to the left it generally alleviates some of the bend and reduces the stress on it.
Having experienced this problem before, the best advice I have is... just keep messing with it until it stops. heh. not much help, I know.
A