I don't think you will find a nice and tidy mechanism for this reaction, though I don't think one cannot come up with a reasonable mechanism. The protection step should be a simple acid catalyzed addition of the (+)CH2OCH3 cation to the alcohol being protected. So you need an acid to generate it from dimethoxymethane. If you used pTsOH, this would work, but it will also give a competing mole of methanol. I anticipate that any methanol being generated can be removed by reacting it with P2O5, the anhydride of phosphoric acid. Its reaction will give some phosphoric acid (or its equivalent) to acid as the mineral acid reacting with the demethoxymethane.
This reaction is an alternative to using chloromethylmethyl ether, a highly carcinogenic reagent.