That's absolutely correct, and they do separate a bit more before going to the huge ovens. There are several burning stages, and you can see how well these places work by the tall chimney and what comes out of it: almost pure water steam. Any other combustion residue gets filtered out so nothing (or as little as possible) is released to the atmosphere. The heat produced by the combustion of all this residue is used to heat water (which can be used for heating, etc).

Or at least that's what they explained during the plant tour I attended in my city about 1 year ago...in Swiss German, of course. I did miss a huge chunk of if, but the pointing and the signs said a lot.