Only occasionally.. When he can't help it.
My guess is that he isn't converting mass into energy, or making a perfect O2 H2 mix.
Do you guys know what Entropy is? Well a basic description is that in the Statistical sense, things tend to go toward a more disordered state, as there are more possibilities in disordered states than a clean state. It's like a dirty room. There's about a bajillion different possibilities that will define your room as "dirty", so it is simply more likely that it will be dirty than clean.
Under this definition of Entropy, it is theoretically possible that for a mixed gas of N2 and O2 in a container, all of the N2 will be on one side, and all of the O2 is on the other side. It's possible, but it's only one possibility out of a bajillion, so it's not ever going to really happen.
All sorts of things are possible but improbable. It is possible that the glass plate next to you suddenly has all of the molecules vibrate exactly right and it randomly changes form. Or it suddenly turns into gas. Or a liquid.
What I believe Soulcasting is, (at least Shallan's) is to "convince" the spren of an object to vibrate just a little bit differently. So it isn't so much that the Flaming Man is actually turned into Fire. It's that Jasnah has convinced the spren to vibrate just a little faster (okay, a LOT faster) so that he burns. So yes, there should be ash (or at least Smoke).
And the reason why there are Ten Essences, is because there are certain vibrational "hot spots". Do you remember Kabsal's demonstration with the cities? How the sand will end up looking JUST like a city if you have the right parameters? This is like the Ten Essences. They are vibrational "Hot Spots" that are easier to find and stay at for the spren.
"Now what about the change in elements? How do you account for the lost protons and electrons?" I don't really know. Perhaps they are changed into the Power of Creation, where they are kept there, until there is a mass increase transformation, and then the Power of Creation is turned into mass. Or maybe it's the Stormlight. Maybe it turns into extra Stormlight and diffusses, or the energy in Stormlight is turned into mass.
I think that Brandon doesn't really Break the Laws of Thermodynamics in his books, as they're just a little bit... different. See the Iron mass/momentum thread, or the Redshift thread, where he tweaks the laws just a titch so that we can have sweet powers- so he can tell dynamic stories.