I've noticed this as well, and someone else already filed a bug report that got accepted.

http://forum.square-enix.com/ffxiv/t...r-every-battle

To add to the information on this: previously there was no BGM inbetween dungeon fights. Battle music played while in combat, then fell silent. Now the dungeon intro music restarts as soon as you are out of combat.

The intro music also plays as you are leaving the dungeon, once you have interacted with the exit portal.

It seems to have priority over normal battle music, but not boss battles.