Just announce you're keeping notes for a project to improve the game, and when you ask for rolls (Initiative, attack rolls, etc.) tell the players you want to hear the actual die roll and then the modified result. Keep notes for a few sessions. If it turns out one player is consistently rolling above average on the unmodified d20, tell that person they are either cheating or have a problem die.
Honestly, from your description, the dude is almost certainly cheating. The issue is whether or not you want to create a major interpersonal issue. I would because that sort of behavior is obnoxious and unfair to the other players, but it's your home and you have to make the decision.