As I was trying to run 4 330mm F10T8 fluorescent tubes in series each with their own starters on a North American preheat CFL HX autotransformer ballast intended for running 2 18w G24D-2 PL-C CFL lamps in series, I have observed that the last tube on the neutral side of the preheat circuit seems to glow dimly for a few seconds and makes the 3 other tubes start up after it establishes a stable arc without its starter kicking in. What causes such startup behavior to happen? Keep in mind that the ballast has a 470v OCV.

Here is my video of my fixture that uses such a circuit:

https://youtu.be/R31D7LP0lGM

What is the OCV at each lampholder?

When I tried measuring the OCV of each set of lampholders, I got some weird readings in which the pair closest to the ballast’s live output was around 59v while the inner pairs of lampholders only had a reading of about 1v to 2v while the lampholder pair next to the ballast’s neutral output was around 4v. However, when I measured the OCV between the lampholder closest to the ballast’s live output and the lampholder closest to the ballast’s neutral output, I got a reading of 470v.

With series lamps calculations like "each lamp needs 200V to cold ignite, so 4 in series would need 4x200V=800V" do not work.
The thing is, the voltage is not evenly distributed across all the lamps. Once you ignite a discharge (ionize the fill) in it, the voltage across that lamp drops a lot. With 4 in series at 400V OCV and 3 of them ionized, for a brief moment (until the ionization decays; which takes few 10 ms mainly when the filaments are already preheated) you get nearly all the OCV across the remaining lamp. And that then becomes enough to ignite it the way you describe.

In fact when you start with all lamps with no ionization at all, the external capacitances makes all terminals at GND level and only the first lamp at the hot side will see the ballast OCV. That will ionize the gas in it. Once ionized, that lamp effectively bypasses its terminals, exposing the second lamp for the full voltage. Then the second lamp ionizes and so the cascade progresses, until it ionizes all the lamps in series. Now it depends, if the OCV is high enough to drive a significant current through all of them in series with cold cathodes, so that current is able to warm them up. If not, the thing will just stay dimply flickering. If yes, all lamps light up.
That way you may reduce the need for really high ignition (or even the reignition one to some extend) voltage, so for series operation you need less OCV than the one needed for a single one multiplied by the number of lamps, so can save on the VA the ballast has to handle, so its losses.
That is, why 4 lamp ballasts become so popular for industrial settings in the US: They are using two lamps in series (there the gain is the greatest) on each branch...