When using Time Machine, does it follow Symbolic Links in mac?

No.

Symbolic links are backed up as-is. This is because on one drive, following those links would create multiple copies of the same file on the backup location, and would wreak havoc the next time you had to restore. If your backup contains symlinks to another volume, restoring from that backup would leave you exactly where you were before, with those links pointing to the other volume.

In System Preferences -> Time Machine -> Options... you have the opportunity to manage whether or not other volumes are backed up. If you would like to back up your music library, just remove the external volume from the exclusion list. If you've got too much other stuff on that same volume, maybe you'll need to further partition your external such that the music volume contains only that.