When the US had conscription was evading the draft prosecuted by federal courts or by courts-martial?
Since the late 19th century, draft evasion has been prosecuted in civilian federal courts. A friend of mine got a year in the poke for refusing to register.
Technically, you’re not subject to military law until you’ve taken your oath and become an official member of the armed forces. So a draft evader would have to be tried under the civilian legal system.