If you knew you were to be conscripted, wouldn't you volunteer preemptively to collect the $50?
Not saying these guys are bending the story a bit to make for a better movie (people I know in Jones County are telling me that the very first time these two showed up locally, they brought a movie producer with them). But it seems like there's room for Newt to have considered himself conscripted even if he volunteered.
That being said, it seems likely, based on when he left the service, that he left due to the 20 slave act.