First, the device is not a water softener, which reduces the levels of hardness ions (both calcium and magnesium) in water.
Stripped of most of the jargon, the claim is that the device causes formation of small particles of aragonite, a calcium carbonate mineral with a different form than the more-common mineral, calcite. In the aragonite form, the particles supposedly don't stick to plumbing materials and thus do not form scale deposits. Magnesium carbonate is much more soluble than calcium carbonate, so little if any magnesium ions form crystals like calcium ions do. Therefore, it would be more appropriate to call this and similar devices "scale reduction" systems rather than water softeners.
There is some evidence that some of these devices do reduce scale formation. I am aware of a study that measured the rate of scale formation on electric water heater elements. Many devices did not work at all, but one reduced scale formation by about 25% (the OP's device was not part of this study).
The main issue is that there is no agreed-upon independent testing procedure to prove scientifically that these devices perform as claimed. When there is, major manufacturers (like GE) will become involved, since chemical-free water treatment is the holy grail for them.