They need settling the entire time transfer is occurring.
Let me ask this another way. Why is the LOX not settled? What is going to unsettle it?
It sounds like you are assuming transfer during an engine burn?
I'm assuming transfer while whatever provides pressurization to the header tank is operating. If they use compressed gas, then they can go at any time. If they rely on autogenous pressurization, then it would be while an engine is running.
My understanding is they are testing with engines off. Fluid transfer under a higher constant acceleration is a solved problem.
Which suggests that they have a means of pressurizing the header tanks without the engines running.
All of this is an aside to my point that this "propellant transfer" appears to be them blowing soda through a straw. At least, that's all my simple mind sees.
Ship #1 tank to ship #2 tank is a variation of ship #1 tank to to ship #1 tank with different positions.
Only if they use the same basic technique. What technique would scale from header tank on the same ship to main tanks on separate ships? In thinking about this some more, two occur to me.
1. They could blow a lot of gas into the source tank while keeping the target tank at a lower pressure. That would produce a flow of gas and liquid to the target tank, with bernoulli grabbing the blobs of liquid in the source tank and moving them to the connection point. The challenge there is keeping the two tanks at a pressure gradient, though simply pumping available gas in the target tank to the source tank should work. For a while, anyway. This could be simulated in IFT-3, though I wouldn't expect much blobbing in the confines of the small header tank.
2. They could seat the propellants in the tanks by slowly spinning the ships and then using pumps to perform a pretty standard transfer, though at lower "gravity". The challenge there is spinning roughly 1300 tons of ship. I don't know how fast they'd have to spin, and I don't know if there are any complications from two connected ships which would be of very dissimilar masses at certain times. The math is fine, but I don't know how it works out in practice (I'm thinking of odd stuff like the Dzhanibekov effect). This could be simulated by spinning Starship 26 and using a pump somewhere in the downcomer to transfer LOX to the main tank. The fact that the header tank is on the center line and the downcomer follows the skin of the ship would make that possible.
Approach 2 seems the far simpler to execute (and simulate), assuming that two connected ships can spin stably.
So if they're actually pursuing a technique that applies to inter-vehicle transfer, then it makes much more sense. I guess we wait and hope. Hope that they pull it off, and that they say something about what they did.
Edit: They vented LOX once they reached orbit. I wonder if that somehow relates to all this. Heh. Could they vent LOX to lower the main tank pressure, resulting in pulling LOX through the header downcomer? I understand that dumping LOX was needed for reentry, but were they trying to kill two birds with one stone? I'm only half serious, but it's a thought.
For that matter, venting the LOX is somewhat like the first technique that I describe above - using a pressure differential to transfer propellant. Venting to space is a pretty good pressure differential. Again, just a thought.