Yes, you're close.
^ = scheduled to start the game.
x = will not start the game (position players only, SP will never have an 'x', RP will never have any symbol)
For starting pitchers the ^ will show up 5 days in advance as they are easy to determine. For position players the ^ or x show up around an hour before game time, as soon as the lineups are submitted. For position players the x means they did not start the game, but it's possible they got in later.
It's not full proof though Zach Duke was scheduled to pitch Sunday's game and he was moved up a day to start Saturday. The ^ was not updated.