If you have parents from the same game, just enter your ID into the box and you should get seeds relevant to your game. However if you have an international parent like Syberia's ditto, you must clear out the ID box otherwise it will mess up your seeds when RNG'ng for the Gender/Nature/Ability.
I guess it makes sense because International parents has a higher chance of giving you a shiny spread. It doesnt make sense if it just gives you the same PID's for an egg.