Generally speaking, it should not be a problem (see Travelling with two different passports). Show the US travel document to the airline when starting the trip back to the US (to prove that you will be able to enter the US and make sure the right document is submitted to the US authorities) and otherwise use whatever document you need to use when crossing a boarder.
Thus when leaving Turkey, if asked by the Turkish border guards, show them the document you used to enter Turkey. The border guards in the country you will enter next probably don't care about any entry/exit stamps from Turkey but if they do you can still show them both your other passport and the document with the Turkish stamps. In most countries, this should be enough to clarify any issue and reasonable requests (e.g. to stamp one passport or the other) will typically be honored.
The only real problem is if you need to hide one of them for some reason (e.g. you are going to a country that makes trouble for people who visited some other country, you want to make sure the US authorities don't know you have been to this unnamed third country, or you want to hide the fact that you have a US re-entry permit). In that case, any discrepancy between the stamps (a dangling exit stamp without entry elsewhere, showing up at a border checkpoint without exit stamp from the country you just left, etc.) could raise questions. Worse case, your luggage could even get searched and the document you wished to hide could be found. It's always risky to try to hide something at a border. But otherwise there is no reason why using several passports should be a problem.