The player who controlled Molten Firebird when it was put into a graveyard will skip their next draw step even if Molten Firebird is returned to the battlefield under a different player’s control (because it’s owned by someone else) or isn’t returned to the battlefield at all (because it left the graveyard before the end of the turn, for example).

The second ability can be activated only if Molten Firebird is on the battlefield.