When people say that they see noise, I have no idea what they are looking at... some people think that any noise at all is bad, that the only good image is noiseless. Yes, there is some visible noise at 800 ISO on the Alexa and it is cleaner at 400 ISO, but whether the noise you see is normal or a mistake, I have no idea. Also, what are you judging the image on?
Just in case, I'd shoot a test on a second Alexa and compare the two, and also shoot both Log-C and Rec.709 and compare the two, and check it on more than one type of monitor. Some post houses use plasma monitors which will show the noise more clearly than an LCD or digital projector. The black levels of the monitor will affect how well you see the noise.
I will say that it isn't unusual for commercials shooting in Rec.709 on the Alexa to stick to 400 ISO to get a clean image.
At 200 ISO, you run the risk of clippy highlights that make the image feel video-ish.