If you use {sorin markov}'s ultimate to control your next opponents turn, and made them do something illegal, who would get disqualified? You are in control, but they are the ones doing the illegal thing.
Straight from the rulings.
You can't make any illegal decisions or illegal choices -- you can't do anything that player couldn't do. You can't make choices or decisions for that player that aren't called for by the game rules or by any cards, permanents, spells, abilities, and so on. If an effect causes another player to make decisions that the affected player would normally make (such as Master Warcraft does), that effect takes precedence. (In other words, if the affected player wouldn't make a decision, you wouldn't make that decision on his or her behalf.) You also can't make any choices or decisions for the player that would be called for by the tournament rules (such as whether to take an intentional draw or whether to call a judge).
Could you make them concede?
Third from last ruling - No, you can't make him concede.