Geomagnetism is easily measurable and has been monitored for a long time.
The central claim is that changes in cosmic ray frequencies can predict earthquakes. The proposed causal mechanism is changes in the geodynamo affecting the propagation of cosmic rays. The effect on cosmic rays is secondary to the changes in geomagnetism. Despite decades of people looking for evidence, changes in geomagnetism are not associated with earthquakes[0].
If this paper's hypothesis is true, geomagnetic fluctuations should co-occur with fluctuations of cosmic ray counts - thus geomagnetic fluctuations should also predict earthquakes. But they don't.
Claims of being able to predict earthquakes have had a long and not great history. Earthquake prediction is the faster-than-light travel of geophysics. Any claims that it is possible should be viewed with extreme scrutiny.
You're incorrect or confused on several aspects so let me break it down for you.
Frequency of detection of secondary cosmic radiation is very sensitive to geomagnetic conditions. That is not up for dispute.
The paper in question provides statistical evidence that "variations of secondary cosmic ray detection rates are periodically correlated with future global earthquake magnitude sum".
The paper contains no claims about precisely predicting seismic activity in terms of geographic location or time of occurrence. The authors make this abundantly clear.
The USGS page you linked has no citations or even a timestamp. I'd wager it hasn't been updated in ages. It's not the decisive source you want it to be.
The linked article fails many test of credemtialing, but most egregious is the entirely fale presemtation of "Geo Cosmo Science and Research Center" (really this: https://www.geocosmo.net) as being a NASA lab.
> The causality they're claiming just does not have any physical plausibility.
Survey the literature and you’ll find plenty of evidence that there is some credence to the idea.