The theory is that solar minimums reduce the solar wind and allow more cosmic rays to reach earth. Some component of them (muons IIRC) can penetrate deep enough to allegedly affect lava reservoirs. That explanation may or may not be correct, but apparently there is some correlation known between solar minimums and volcanic activity and/or quakes.
Reducing the solar wind should make it harder for cosmic rays to penetrate. The solar wind deforms the Earth’s magnetic field, “pushing” it away from the Sun and thinning it on the Sun side.