I am using a Lumia phone. I think the reason might be that the phone does some strange stuff with the Aux's GND when supposed to mute the sound. I will test the radio with some other source of sound and will see then.
In the meantime I've also tried to resolder the GND cable, solder it directly to the TDA7313's GND pin, then behing an elko which is connected to that pin, and even between the LOUD R and LOUD L pins (as found on one of the photos of the e30-talk tutorial) - no change...
the only thing I managed to achieve (when the Aux GND was soldered behing that elko, which is connected to the 7313's GND) was that the interference was a bit "smoother"
I already got an advice, that if this persists with other devices, I should try to add some elkos to the R and L channel...