It's because desmopressin stimulates ACTH release in corticotrophs (normal cells) and in corticotrophinomas, i.e., tumor cells in the case of Cushing's disease. This effect has been shown to be higher in CD than in non-CD patients. However, I think the ability of the DDAVP test to discriminate between CD and non-CD is questionable, although I'm not too familiar with that area of the literature.
What does your MRI say?