Persephone Super Moves in 2v2
Game creator David Sirlin answered both of these questions recently on the forums.

1) Persephone controls the opponent on the following turn from the bench.


  Abilities work from the bench. It says you control their turn.


2)  Mistress's Command (and Onimaru's Clockwork Soldiers) intentionally do 1 damage and there is no minimum associated with the rounding of the Super Cancel Tag specifically so that its effect will not trigger in such a scenario.


  "Rounded down" is specifically so that MC and CS do 0. Very much on
  purpose.