Title is worded a bit misleadingly, it sounds like something from outer space causes earthquakes, but it's not the case:
[...] any substantial earthquakes linked to disturbances in the Earth’s dynamo flows would alter the magnetic field, thus impacting the path of primary cosmic radiation. The fallout of these alterations would be apparent in the changes in the counts of secondary cosmic ray particles recorded by ground-based detectors.
So as I understand, when an earthquake happens, it also disturbs the magnetic field of Earth, and you can measure this disturbance by measuring cosmic radiation.
The magnetic field changes ~15 days before an earthquake happens.
Stuff moving around in the outer core changes the magnetic field.
So looking for patterns in the data from cosmic ray detectors can tell us something about what's going on in the core, which is predictive of when an earthquake is about to happen . . . somewhere.