Voluntary departure so confusing?

my fiance was granted voluntary depature from judge. i was going to buy ticket but his deportation officer told us we dont need to buy it, that since he is going to mx, he can be put on govt plane. only diffrence is he has to sign paper agreeing to go with hand cuffs/shackles. but vd will still be honored. does this happen? we want to be able to file for him to come back to our son and me. he has no crminal records only coming illegally 10yrs ago