It's always on his record, so it won't go away in that sense. But he served his time for it, the time that Baseball itself imposed on him, and now his slate is clean, and now he gets to move on with his life.
And your 100% certainty to the contrary, I don't believe Hinch never told the players he was against the scheme. His actions (e.g., smashing the monitors they used to see the stolen signs) say otherwise, so again, that simply makes no sense.
Look, if you hate the Tigers so much because they disrespected you by hiring someone you despise, then maybe this isn't the team for you. If you want to follow a team you respect, maybe consider following some other team. The Twins are doing pretty good these days.