We checked the Colors in Color Think and find out, that the colors that adobe display out of gamut from the Adobe RGB working space were actually out of gamut. (mostly Cyan is out of gamut)
As you said:-
If you change your PS working space to be ProPhoto (16 bit) none of your real Lab colours should flag up as OoG and should transfer almost exactly.
So, we changed our working space from Adobe RGB to Pro Photo so that colors fall in the gamut. But even using Pro Photo it still shows the color out of gamut.
Is there any specific color setting in Adobe for Pro Photo working space or there is any other mistake we doing?