The time is on the vertical axis, the frequencies on the horizontal axis.
The lines are sloped, which indicates an acceleration of the spacecraft w.r.t. the observer due to Doppler shift. In the second figure in the tweet, they show that the lines suddenly become vertical again, indicating that there is little to no acceleration anymore. Such a sudden change in the slope is quite charactersitic of an engine start/cutoff/throttle. If you only know the slope (not such a sudden change), then caution is advised, as it is not uncommon for transmitters to adapt their frequency to their relative velocity (such that a receiving base station on Earth only has to tune to one specific frequency and not compensate for the Doppler shift on such weak signals), and just moving throughout the orbit will also change your velocity w.r.t. the observer without having to fire your engine.
As for the LOI, I have no knowledge about that so the following sentence is a hypothesis which could be completely wrong. If AMSAT-DL actually saw the LOI, I would think that to land on the south pole you need to enter a polar orbit, which when coming from Earth you would probably need to fire your engine near the north or south pole, which would be in line of sight of the ground station. But that last part could be completely wrong.