In order to install the Mod properly, so the Leader Music will be played you must do the following:

1. In Chile's Mod Folder, search for the ChileMusic.txt and ChileMusicDefines.txt and open them.
2. In your Civilization Install Directory search for the following:
"(Install Directory)\assets\DLC\Expansion\Sounds\XML"
3. Open Audio2DScriptsExpansion1.xml and AudioDefinesExpansion1.xml from that folder
4. On Audio2DScriptsExpansion1.xml, paste the contents of ChileMusic.txt under <Script2DSounds>
5. On AudioDefinesExpansion1.xml, paste the contents of ChileMusicDefines.txt under <SoundDatas>
6. Save both files and enjoy your new civ with its own leader music.