I do not understand what you by "digital pots cannot handle a signal outside their supply range"
The chip is powered by a 5V supply referenced to ground. So any signal you apply to it must be above 0V and below 5V.
The audio signal I generate and use a input for this circuit has a range from 0 to 5V.
If this is so, and it is highly unusual, then you are shorting the DC bias on that signal to ground with your ground connection on the Audio Input socket.
Audio signals go above and below their DC reference point, so a voltage range from 0 to 5V should have a DC reference point at 2.5V. This is the point you are connecting to your Arduino's ground.
If your Audio signal that you apply to this is totally isolated from your Arduino's power supply then you will be applying negitave voltages to the chip's input, which will damage it. If it is not an isolated supply you will be damaging your audio signal generator and could damage that.
The key to fixing this is to AC couple the audio into the chip. ( using a series capacitor ) and then add a DC bias to the input of the chip with a 10K pull up and a 10K pull down on the input. It would be good to also AC couple the output of that chip to the output socket.