Yes, you can and should use the DD-1 on your DSP as well.
Treat your DSP as a headunit, use the 0db tone and the appropriate tone for the appropriate channel outputs (IE, 1khz for front/rear dedicated dsp outputs, and 40hz for dedicated sub outputs on your dsp), this way you have the maximum clean a/c voltage output from your DSP. Also make sure all EQs on the DSP are flat when doing this as well!
Now the one thing to be careful of is the a/c voltage output, you don't want to set it higher than your amps inputs can handle, so after tuning with the DD-1 you may want to check the rca a/c voltage output of the DSP because the DSP can and will take your 4v rca signal and turn it into 6-9+ volts output. So if your amps can only handle a 5volt input then you will want to back the voltage down some on the DSP, and then go and match voltage for each output.
Then use the DD-1 on your amplifiers using the appropriate tones with your desired gain overlap setting (-5db, -10db, etc).
I think my Audison Bitone DSP was putting out 11.7 volts clean when tuned with my DD-1 but I backed all the levels down to 4.5volts that I verified with my multimeter and then I have my amp gains up about 1/8, its very very little.