I have a similar installation (no gen-turi as yet), and have never had any noticeable problems nor any CO alarms using the generator. Obviously I don't open the window directly above when running it.
I suspect the exhaust for the main engine also terminates at about the same distance from the vehicle in a different location. The two are not entirely comparable, of course; the main engine is mostly used when you are in motion, and perhaps more to the point the catalytic converter system means that there is basically no CO coming out the exhaust pipe. Neither applies to the generator, though if it's tuned and running properly it should not be producing much CO...but it doesn't take all that much to be dangerous, either.