Sulfate salts of magnesium and sodium
Solubilities (taken from Wikipedia):


MgSO4: 35.1 g/100 mL (20 °C)
Na2SO4: 13.9 g/100 mL (20 °C)


It does seem that the solubilities should be  an order of magnitude higher than  is quoted in the paper you are reading.

Several ideas:


The paper is wrong.
You did not understand the paper correctly.
The solubilities mentioned above are of the pure compound in pure water. If it's in an evaporite basin the the chemistry of the water might differ and the solubilities might also differ.
As an example, the presence of a more soluble salt will cause the less soluble salt to be come even more soluble (a process called "salting-out"). For instance, if you have an almost saturared solution of NaCl, and you add CaCl2, a more soluble salt, you will start preciptating NaCl once enough CaCl2 is added to the system.
There could be other anions in the system which make Na and Mg less soluble. Borates? Phosphates? Carbonates? Fluorides? The solubility is determined by the least soluble component of the system. Adding sulfate to magnesium silicate isn't going to do much to it in terms of solubility (unless it is sulfuric acid of course).