If the state has a "mandatory minimum" sentence does that mean the inmate WILL definitely have to serve that amount of time ?

Without knowing more about your inmate's particular sentence, the mandatory minimum means exactly how it sounds. If the offender is guilty of a charge with a mandatory minimum sentence, the judge is pretty much duty-bound to follow the sentencing guidelines of the state. The judge does not get to interject his "judgement" if leniency is their preference, the law stops them from deviating.