Causality is probably the wrong way to think about what's going on. You get counterintuitive answers when you try and describe many quantum processes that way, and in terms of relativity, what the experiment is saying is the same as previous results.
When A and B happen at different points (a and b) in space and time, there are three possibilities:
1) After A, light could travel from a to b before B: In that case, A happens before B to all observers. A can affect B.
2) After B, light could travel from b to a before A: in that case, B happens before A to all observers. B can affect A.
3) Neither is true. In that case, different observers might disagree on which one happened first; neither one can affect the other. However, all observers will be able to calculate that some observers will have a different view of the situation than they do.
However, quantum entanglement allows "action at a distance", which is a way of letting A and B affect each other in category 3. We do not currently understand why this is true; models incorporate it, experiments verify it, and it works mathematically, but we have no good intuition for why this should be true.
Previous experiments testing entanglement used a situation in which, to an observer in the laboratory, A appeared to happen before B, yet with a small enough separation that it fell into category 3), not category 1). As a result, in previous experiments, an observer traveling at the right velocity would have seen B appear to happen before A. So, we would expect the result should be the same if B were, to the laboratory observer, slightly before instead of after A, yet still in category 3). And, that experiment has now been done, and this turns out to be the case.