Is this correct or have I misinterpreted the info? Hope you can set things straight.
When you're talking about this anionic transformation, it happens in a stepwise fashion--in effect the stuff acts as a weak base. So you start with, at very high pH, SiO3 (2-). As you lower the pH some of this converts to HSiO3 (1-) by abstracting a proton from solution. So you end up with a ratio of HSiO3(1-)/SiO3(2-) which increases with decreasing pH. When the ratio collapses and you end up with 100% SiO3(1-) in solution if you decrease the pH even further you will start a new ratio of H2SiO3(solid)/SiO3(1-) and the stuff will start to precipitate out.
If you look at the charge on magnesium it's 2+, so what's happening here is that in the HSiO3(1-) form the anion can effectively chelate the magnesium (2 equivalents per Mg cation). but once you have SiO3(2-) in solution the anion and cation can start to form strong ionic bonds, which can cause them to precipitate out.
Adding other cations/anions to solution can muddle the predictive process here.
If you look at your second graph you can still have a pH above 8.00 and keep the stuff soluble. When you hit a pH around 8.75 the HSiO3(1-) starts giving up protons and converting to the (2-) form. That's when you'll start to get magnesium salts.
To be clear, this is probably a faulty explanation because Sillicic acid actually acts very strangely in solution and forms complex structures which interact with each other. It really is weird stuff. When you add a bunch of other stuff to it the thermodynamics become totally unworkable from a theoretical point of view--and that's why experimentation becomes necessary.
So while these transformations/ratios I've described might not accurately depict what is actually happening--this is the general thermodynamic form you are looking at from an idealized perspective.
I couldn't find pKa/pKb values for the stuff so it's tough to say at what pH what is happening. I think the general idea here is to keep the concentrations low to avoid all of this mess. The sweet spot for maximum solubility, if you superimpose both of these graphs, appears to be somewhere in the 8.5-8.75 pH range.