I'm by no means an expert in quantum physics, which makes my lack of surprise at this fairly uninteresting, but it seems to me these results are completely compatible with the time-symmetric interpretation of quantum mechanics. If I understand it correctly, according to TSQM the particle already "knows" about its future interactions to the extent that quantum information is preserved through any intervening interactions. So in the case of photon-splitting, the photons leave their source with polarizations that are aligned with (or opposite) the axis on which they will be measured. You could say the information "propagates" in both temporal directions, but I think it makes more sense to think of the particle's entire timeline as a single entity.
According to the papers I've read on TSQM, it makes (or made) no predictions that are different from the Copenhagen interpretation. This experiment seems like it may be the first to show a difference. Not necessarily because of any predictions, but because of the additional mental contortions required to hang on to the Copenhagen interpretation. There's still no ability to send "real" information faster than light or backward in time, though. I say this only because of the purported equivalence between TSQM and Copenhagen, not because I have any idea why it should be the case. Intuitively, it seems like it could be related to the (quantum) information-theoretic version of entropy that you get with reversible computations. Or maybe even just real entropy, since TSQM still "behaves" as if it's nondeterministic from our perspective, since we can never know enough about a system to know its "true" internal state. So somehow everything conspires to prevent us from setting up a system that would carry some piece of information back in time that we care about.
I guess another way to look at it is that the universe is a solution to some kind of differential equation. Possible solutions that contain paradoxes aren't valid, so they don't happen. Not via some shift in some "unified" timeline ala Star Trek, but through colossal numbers of tiny shifts that disperse any information that we're trying to send back in time that would cause any kind of paradox at any scale. The result is a universe that appears to have an arrow of time at any scale we can actually measure, appears to mostly follow General Relativity, etc. Until you get to scales, large and small, where the exact underlying geometry starts to matter.
Come to think of it, if paradoxes are what's important, the ability to send information back in your own timeline (i.e. within your own past light cone) is all that matters. If there is no privileged reference frame, this also means you can't send information into spacelike regions of your own light cone, because if two entities do that then you can arrange things to send information into your own past light cone. But if there IS a privileged reference frame, say, the reference frame of the CMB, where you can't send information into *its* past light cone, then you can send information faster than light but still not into your own past. Recall that the Lorentz transformations were initially introduced to (successfully) explain how light could appear to always be moving the same speed even with a luminiferous ether, but then Einstein discarded the luminiferous ether because he realized it wasn't necessary, not because there was any evidence that contradicted it.