I thought there was a specific order to this, but honestly I can't find it. You want to interact with the pillars until they're throwing up a higher/brighter light (which can take a little bit of a delay). Keep interacting with the pillars that aren't glowing or aren't glowing as brightly until they all flash and then go dim and the middle actually says something about the face. If you don't have the item from Jordine to complete the interaction with the center, you may need to grab it from him.
Good luck, and I hope someone finds a clearer explanation than mine. The YouTube videos I've seen so far don't feel very helpful.
The stone has more brilliance when the light is correct. When pressing a stone the light is exchanged with the stone on the right. We have to exchange them until they are all shiny.
I can confirm this works, even if the lights don't show up afterwards just wait a bit and then talk to the thing in the middle as soon as it's possible. This will complete the quest. Thanks a lot for that screenshot!