Thank you for the various replies on the matter!
The feat seems quite rude for a spectator due to its nature of treating him and his vest, so I have never witnessed it performed on stage, but once in a circus performed by a clown as a comic act.
Recently I found it performed in Wellington, New Zealand, on 5 May 1868 by a Japanese performer of the Royal Tycoon Troupe of Japanese, as shown below. (Wellington Independent, page 5)
One of the prettiest was the extinguishing of lighted tapers by an arrow shot from a bow, in one instance the arrow being fired from between the marksmans legs. In order to prove that there was no deception, any person among the audience was invited to walk up on the stage and hold a taper while it was being fired at. Some courageous gentleman did so, when the light was duly extinguished, and in reward for his intrepidity, a performer seized hold of him, and turned his waistcoat inside out without taking off his coat, and the unfortunate man returned to his seat apparelled somewhat differently to what he was when he left it.
The troupe left Japan just after Japan opened her country. So, I believe this feat had long performed before it as a well-known stunt in this isolated nation from Western countries.
Could I understand that his coat means his waistcoat, both of which appeared in the newspaper clip telling he turned his waistcoat inside out without taking off his coat?
I assume so because any audience in the theatre never wears an overcoat on his vest especially when he volunteered on stage.
This is why I dont think that the stunt making the vest inside out was different from the one described in Cremers Magicians Own Book and other earlier book, in which "TO TAKE A MAN'S VEST (or shirt) OFF WITHOUT REMOVING HIS COAT (overcoat)" was explained.
If my theory is correct, the first recorded performance of the feat up until now might be of Mystic DeVere Simmonds in 1918.