SBM -
According to that link that's exactly when you probably had it done, when you had bloodwork taken. "on enlistment, reenlistment, and deployment" are the times when it's taken. Refusal nets a courtmartialing.
"What was then called the DOD DNA Registry, a program within the Armed Forces Institute of pathology, was established pursuant to a December 16, 1991 memorandum of the Deputy Secretary of Defense. Under this program, DNA specimens are collected from active duty and reserve military personnel upon their enlistment, reenlistment, or preparation for operational deployment. "
"Two members of the United States Marine Corps were ordered to give DNA samples before being deployed to the Pacific in January 1995. They refused to do so and were charged with the violation of an order from a superior commissioned officer. The military court martial dismissed the charges, holding that the regulations underlying the DNA Repository program were not punitive and thus no disciplinary action could be taken for refusal to provide specimens. The two Marines sued the government in federal court, charging that the DNA collection program violates the Fourth Amendment protection against unreasonable searches and seizures. The district court found the DNA collection requirement to be valid. The court of appeals declared the case to be moot because by the time of the appeal the two Marines had been granted honorable discharges without ever having given samples of their DNA. Since that time two other members of the military have refused to give their DNA samples. One was sentenced by a court martial to 14 days hard labor and a two-grade reduction in rank. Another temporarily lost his rank and 40 percent of his pay, and was reassigned. He was later able to claim a narrow exception on religious grounds and was reinstated. "