Correlation as used here and put simply means that when the signal coming out of one the detectors increases, the signal coming out of the other detector (which is physically separated from the first detector by a very large distance) also increases, and when the signal coming out of the first detector decreases the signal coming out of the second detector also decreases.
The existence of that mathematical correlation between those two signals coming out of those two remote detectors absolutely implies there is a causation to the correlation (yes, mathematical correlation can imply a causation, even while it alone is not able to indicate what that causation is).
The question at hand is not whether there is a correlation or whether there is a causation. The question is what is the causation for the correlation and whether that causation is a gravity wave or something else.
The odds are extremely good that that causation is a gravity wave, but it's a big enough experiment and a big enough result that it's worth looking very closely at the analyses that argue in favor of it being a gravity wave (and those that argue against it).