What is a digital common?
You can look at this as well: https://www.benthowave.com/products/Specs/Hydrophone%20Wiring.pdf

Common is the GND for the power; You put your battery between +VDC pin and Common.
Digital Common is the GND for the digital inputs; You connect your digital outputs to A1 and A0 and the GND of the driver to Digital Common.
Output Signal Common is the GND for the output signal; You measure the output between the Output Signal pin and Output Signal Common.

I'm guessing the Common and Digital Common is connected directly inside the instrument. But, you can't use the Common as a connection for you digital interface because its a battery terminal to which the battery is connected to. Maybe the battery is even internally housed in the instrument, so you can't eve access that pin from the outside?