From my electronics background, here is my assessment. First off, you have to remmeber that USB port on your car stereo technically can be used for charging, but thats not why it was put on there. The TB uses power faster than the DInc and I would guess that when it is trying to charge, it attempts to suck more power from the charger also. The TB is probably trying to pull an amount of power that the circuitry in your car stereo is not made to put out. The car stereo probably has protective circuitry so that when a certain threshold of current is hit by the USB port, it cuts the power to it to protect it's own circuitry. Which would explain why it momentarily starts to charge, then stops.
Like somebody said above, just buy a good charger off amazon for 5 bucks before you jack your car stereo up.