The tentative causal explanation is to do with the 'piezo-electric effect'. https://en.wikipedia.org/wiki/Piezoelectricity For example, when the crystal in a cigarette lighter is compressed it emits a spark, because the mechanical force is transformed into electrical energy.
Conversely, if an electric charge is applied to the crystal, it will change shape slightly to absorb the energy; so, given that the Earth is magnetic because of what is assumed to be an iron core, if the power of a solar flare hits the planet's magnetic field then it is possible that there is some expansion or warping deep inside that returns to the surface in the form of earthquakes and volcanic activity.
This connection between the sun and the Earth's seismic activity has long been suspected by 'Dutchinse' (Michael Yuri Janitch) an American amateur earthquake analyst and predictor and the new study has excited him:
He has also previously suggested - as have some others - that a scientific program known as HAARP, which studies the effects of powerful man-made radio emissions aimed at the Earth's ionosphere (upper atmosphere) may have an effect on seismic activity and weather and may even be part of a clandestine military project. This is pooh-poohed by mainstream commentators (e.g. here), though of course it's not axiomatic that all conspiracy theories are wrong.
As it happens, the sun is unusually 'quiet' at the moment (i.e. few sunspots, flares and CMEs); and there seems to be a correlation between the sun's c. 11-year sunspot cycle and climate on Earth - these quiet periods are associated with cooler weather - there was a particularly long time from c. 1645 on:
'One interesting aspect of solar cycles is that the sun went through a period of near zero sunspot activity from about 1645 to 1715. This period of sunspot minima is called the Maunder Minimum. The "Little Ice Age" occurred over parts of Earth during the Maunder Minimum.'
- and the same article says times of high sunspot activity may warm the atmosphere, instead:
'There is debate within the scientific community how much solar activity can, or does affect Earth's climate. There is research which shows evidence that Earth's climate is sensitive to very weak changes in the Sun's energy output over time frames of 10s and 100s of years. Times of maximum sunspot activity are associated with a very slight increase in the energy output from the sun. Ultraviolet radiation increases dramatically during high sunspot activity, which can have a large effect on the Earth's atmosphere.'
However, NASA suggests that the current scale of 'global warming' is not related to variations in the sun's radiance: