Generally speaking, DUI's on a military base for civilians or otherwise are handled the same way a DUI is handled off a military base. You were probably agreed to attend court in a normal civilian court. You are not subject to military prosecution, because you are not in the military. Best suggestion: talk to a lawyer in your area who specializes in DUI law.
When interviewing a DUI defense lawyer ask the following questions:
What percentage of your annual caseload is relegated to defending DUI?
How many DUI jury trials did you have in the past 12 months?
Can you provide a list of DUI training seminars or conferences attended in the past 2 to 5 years?
What percentage of your clients enter a plea of guilty to the crime charged?
Have you or any members of your firm written articles or books related to defending DUIs?
How many lawyers are in the firm, and are they all DUI defense attorneys? If so, will they collaborate with their colleagues about your DUI case?
How many years have you defended DUI cases?