This point is clearly addressed in the paper: The ends of the tube can slide 300 meters next to the station, and the tube is not firmly attached to the pylons but can move to accommodate the expansion.
"These would absorb the small length changes between pylons due to thermal changes, as well as long form subtle height changes." [emphasis added]
The cumulative expansion is dealt with in a single sentence:
"A telescoping tube, similar to the boxy ones used to access airplanes at airports would be needed at the end stations to address the cumulative length change of the tube."
But that's not enough. The entire track near the ends is moving by this amount. That means that the ends of the track are advancing and retreating over multiple pylons (unless you can figure out a way to cantilever the track over 300 meters). This is a completely unsolved problem.
edit: in retrospect, I can clearly see the problem with expanding shaped tracks.
What happens to a long S-shaped track? Think about expanding each segment of the top curve... the turn radius increases and as does the length of the turn. How do you support a tube that can get longer, move outwards along the curve, and change angles at various points? S is just an example, it seems to be a problem with any number of turns (including 1)...
I suppose one option is to simply put it underground to stabilize ambient heat input, and use heat extractors to manage heat generated by the train. If the system shuts down, there might be some thermal contraction but that's easier to manage (it's OK for track segments to separate when trains aren't running - just warm them up before operation)
It's still an issue that at bends of this diameter, the approximation sin(x) = x is pretty accurate, which means it takes 300m of height difference to deal with 300m of thermal expansion. It might be workable to change that to e.g. 100 bumps of 3m.
"As land slowly settles to a new position over time, the damper neutral position can be adjusted accordingly."
And if that doesn't work, the tube can have some kind of rails or just to roll over wheels on top of the pylons. (my own thoughts as non expert)
Rocket engineers with advanced simulation tools[0] have been working on this for 5 months before releasing the paper. Do you really think they somehow missed this obvious issue?
[0] https://www.youtube.com/watch?v=vYA0f6R5KAI
Edit: Further in the paper it says: "The tube will be supported by pillars which constrain the tube in the vertical direction but allow longitudinal slip for thermal expansion as well as dampened lateral slip to reduce the risk posed by earthquakes."
So pretty much what I've said. The other quoted sentence refers to placement of pylons themselves.