WHEN ARE YOU VIOLATING THE COPYRIGHTS?

EXAMPLE: I write a song, here in our very small country: BELGIUM.
Someone living in the USA, hears me playing that song. I was, lucky for me, able to handle this song when I wrote it, to the national organisation, called SABAM, here. In contrary to my performance, the US citizen can't forget the tune, he doesn't even remember that he heard me playing that song, and works it out, very professional, with very good structures, harmonies and arrangements, handling the song (lyrics can be entirely different) to the copyright organisation in the USA, and by coincidence his song becomes a million seller. WHERE AM I STANDING IN THIS PICTURE, with proof I handled it first. When you write a song, do you have to handle this song only in your country, or in other countries as well?