Totally normal, much cleaner than I've seen in similar situations.
Cinestyle raises the shadows and along with them the noise. The 5DIII has a ton of read noise so it's very grainy in the shadows at all ISOs. Even in neutral mode you can see it. With cinestyle and HTP it will be the noisiest camera you've seen at low ISOs and the noise is mighty chunky.
Because you're shooting cinestyle (which is designed specifically and exclusively for integrating into a log workflow) I'm assuming this is b-camera for a 35mm or Alexa shoot, in which case your post house will take care of it with NR anyway. And if you meter properly those shadows will be dark enough that, once graded, they will not be a problem. So I wouldn't sweat it. If it's just test footage to try out cinegamma, well, turn cinegamma off and shoot neutral. And meter.