Your J0408 main cabinet is a DSU II cabinet that can run Impact, Digitech, or Impression phones. The G0408 is a DSU (not a II) that run all of those phones as well, depending on the software cartridge. You use a GM408 expansion on a DSU (G0408, G0816, etc...). You use the JM expansions on a DSU II (J0408, J0816, etc..). The ATI-D should work fine on either a DSU or a DSU II.
Hope that helps to clarify things.