If neutrons are on the list, how are they ruled out from a random decay event emitting particles, from some mineral in the surrounding rock?

The detector from which data is taken to do this analysis contains 7 tons of liquid xenon. It is inside of a larger detector, which contains hundreds of tons of water and more than 10 tons of a scintillator. One of the functions of that outer detector is to absorb neutrons and other infiltrates coming from the rock.

When doing this kind of thing, the analysts will plot the rate of events as a function of "distance from the outer surface" and confirm that it decreases, and in this case "is 0" inside of the detector used for analysis.

But keep in mind that all statements are made statistically, so it's not that the event _can't_ be an external neutron, but that it is _very_ unlikely to be.

They have a lot of shielding for the detector, and also if there were a significant source of neutrons they'd expect to see other evidence, both in the detector and in the separate "veto" detector that surrounds the main detector.

That's not to say it can't be a neutron, but it would be surprising if it were.

The experiment is set up to make any already understood interactions some combination of easy to identify or extremely improbable.