What's the gamut warning before the saturation adjustment?
There is a small (not null) difference in the gamut warning before the saturation adjustment, due to the fact that the red channel is not the only one involved. Sometimes we think about blown channels when they reach saturation (255) but not when they reach zero (0).
What happens is that the mathematical conversion of a specific color from one color space to the other could result in a negative theoretical value in one of the channels (this can be easily tested using Bruce Lindbloom
CIE Color Calculator). In this case the value is set to zero (0) and it doesn't look as a blown out value, but it is a different color than it should be. How far is this color? It is not possible to determine with the gamut warning.
As an example, a sample value from the chest area has R=174; G=44; B=22 in ProPhotoRGB. The theoretical value for AdobeRGB would be R=215; G=-71
; B=8 and for sRGB R=254; G=-69
; B=10. The resulting images in PS will show the Adobe RGB image with G=0 and the red channel below saturation and the sRGB image with G=0 and the Red channel clipped. Both are really out of gamut, but the fact that the Red channel is not clipped in the AdobeRGB version make it look as it is inside the gamut of AdobeRGB.
To show this, the attached files show the red and green channels using the threshold function of PS to show red areas a 255 and green areas at 0. The original ProPHotoRGB version don't have either red values at 255 nor green values at 0. This images show how large is the effect of the green channel.
The AdobeRGB version is at the left, the sRGB to the right. First image shows Red channel threshold at 255, the other the green channel threshold at 0.