I'm probably not the best one to respond but I just can't let a thread sit with no responses.

While not currently on a mission for your city, enter Lower Delkfutt's Tower and you should get a CS. After the CS ends, go to Upper Jeuno and speak to Monbereau (sp?) in the Infirmary. You'll see another cutscene. Next, go to Ru'Lude Gardens and speak to the man who mumbles something about Emptyness in the Arch Duke's place. When you finish this, you should be able to access the Promyvions.

Again, I may be (am probably) wrong so don't quote me on that.