Hi @Alessandro, how did things turn out afterwards, your last update was a while back.
I must confess that I didn’t quite get what I was looking at in the first few shots you made, but it became clearer later on. It seems to me to be a white colour balance issue, the image that your eyes and the camera you used to take the combined wall / iPhone display shot see is in a different color balance, and the iPhone camera is correcting the color balance and showing you the image as it should be. I have no idea however what could be causing this though.
When you say you played with those settings, I take it you mean the standard controls in the Projector settings? Or did you try the instructions here:
I’m really curious about your current status.