The bottles are connected with a circular pipe. The bottles are placed at different height, low and lower at regular interval. They cannot be moved because there are 2 openings in it for the horizontal pipe.
It looks to me the horizontal connecting pipe plays the role of communicating vessels. In this case the pink oil in the lamps is too low in the pictures, it should go over the horizontal pipe.
That would mean that the system is designed in such a way that all lamps have the same level of oil when filled. The lamps will burn a different amount of oil (and time) because the lamps are positioned at different height.
Now we have the radial pipes. Are they pipes? Or simply a structural hanging system. The fact that the same configuration, with a central "tank" is common to both pictures (and to a 3rd not posted here) makes me think that the radial system is made up of pipes. It means each bottle has 3 side holes (2 for the horizontal pipes + 1 for the radial)
It looks like the oil filling procedure is done by filling the central tank. The oil flows by gravity from the central tank into the bottles, equally filled because of the communicating vessel effect.
But then, why are the radial pipes connected to the central tank at mid height and to its bottom? Is this a kind of decantor?
How do you open the central tank? (it is hanged) Do you need to take the whole chandelier down?
If one fills the central tank, it may happen that the quantity inside the bottles gets much higher than expected. There is no apparent system to regulate the quantity of oil in the bottles, only that the quantity is the same.
IOW if I understand clearly the system is made to regulate the gap between the extinction of the bottles. It determines a duration, but does not determine when this duration will begin.
And when you fill the system, How does the air go out? I mean, the air that is in the closed bottles, does it go out through the cap of the bottle?