The rule about a batter hitting the ball with a foot entirely on the ground outside the batter's box applies to ANY bat/ball contact. Whether the ball travels fair or foul, the batter is still out.
Hitting the ball while a foot is touching home plate is a different matter. There is a different interpretation in the "Official Baseball Rules" (OBR), the rules upon which professional baseball are based. There, if a portion of the foot is touching the plate, but the rest of the foot is still in the batter's box, there is no rule violation. Little League Baseball follows the OBR rule. Many of their Little League Softball rules are derived from their baseball rules, so they have a different interpretation from what you see in the rest of the softball world.
For most all others- ASA, NFHS, NSA, USSSA, etc.- hitting the ball with any portion of the foot touching the plate, even if the rest of the foot is still in the box, is illegal and the batter is out.