Did you ever resolve this problem? I also have a Benchmark Media DAC3 and it works great.
With the Benchmark DAC volume turned all the way down, try turning up the volume on the iPhone/iPad to its maximum after you connect the Apple USB3 camera adaptor to the DAC. Then turn up the volume on the Benchmark DAC.
With the Benchmark DAC volume turned all the way down, try turning up the volume on the iPhone/iPad to its maximum after you connect the Apple USB3 camera adaptor to the DAC. Then turn up the volume on the Benchmark DAC.