The experiment involves thinking of the photon as a wave interfering with itself between two experimental stations. The experimenters can adjust the phase of the waveform locally to determin where the particle manifests. The changes they make locally to the phase of the waveform should propagate towards the other experimenter at the speed of light because the waveform is an electromagnetic wave (I suspect this manifests as a slightly higher or lower energy photon briefly as the change in phase propagates because the phase change region is essentially a brief bit of shorter or longer wavelength waveform).
The experimenters can certainly each measure the photon’s position before the speed of light would allow for conventional information propagation (nothing stops them from doing so), but they won’t get the other party’s message if they do because the phase change won’t have propagated to their end yet.
Ok, so far so good - we’re safe, no FTL communications. But we just concluded that these two measurements are made on one photon and are essentially decoupled because the E/M wave hasn’t propagated the phase change yet. That means there could be scenarios where both experimenters get the photon or neither experimenter gets the photon. But there is only one photon and only enough energy for one photon (we change the phase slowly enough to make sure we don’t add a second photon’s worth of energy). So we’re cool on FTL but just violated conservation of energy, which is also kind of a big no no. It seems like you can either conserve energy or FTL but not both.
I’m sure this will all get worked out and submitted to Physical Review Letters and odds are good both FTL and conservation of energy will be safe from disruption, but it’s definitely fun to think about.