Could Na+ ions in water used with a humidifier cause dust everywhere? We have very dry air in our small family house. 

So we bought a humidifier ( https://www.klarstein.com/All-products/Monaco-Digital-Ultrasound-Humidifier-White.html )

But here comes the issue: the tap water is very hard and this causes that dust is everywhere.. due to the humidifier + hard tap water.. like everywhere, even the notebooks fan are full of the white dust, overheating, brutal. 

So we need to buy a "water-softener" ex.: "BlueSoft S30 SVR34" ( http://euro-clear.eu/uploads/content/catalog/EC_residential_product_catalog.pdf )

But: I can read that this "water-softener" device "replaces the Ca++ and Mg++ to Na+ ions"

The big question to chemistry: if the water will have many "Na+ ions" and not "Ca++ and Mg++" ions, would it solve the "dust" issue? So we will won't have any more white dust everywhere, if the humidifier is turned on? 

We already asked the vendor, but they are not sure that this will solve the issue.
In the end, the solution was that instead of using an "ultrasound" based humidifier, we bought "evaporative humidifier". 

delete this line if it cannot be said, but we bought a "trotec aw 10 s"