Looking at how the wires are connected to the tubes....it looks like they are the same polarity or at the very least ,the outer tube of one tube set is the same polarity of the inner tube of the adjacent tube set.
I haven't seen anybody talk about the function of having the tubes wired that way but it looks like they are effectively wired for the same polarity In some way.
I've been thinking about the possibility of free electron build up on one of the electrodes, relative to the other. Cross wiring them like seen in his pictures would prevent sparking through the water, in a given tube set. But the inductive bends in the jumpers could cause the array to act as a pulse forming network. This might be important for balancing the impedance to an input PFN.
Here's an example of the type of balun I was remembering:
(https://s20.postimg.org/5n4wwfay5/balun2_1.gif)
Maybe a little far fetched, without a top connection except through the water.
I just started a new project involving a hidden wire inside the inner tube. A pure static charge on this wire would place the same static polarity on the outside of each electrode tube. But the inside surface of the outer tube would be the opposite polarity. This, in itself, will polarize the water, and also present the sparking hazzard.