This technique appeared in an unpublished notebook circa 1800. Will Houstoun transcribed the anonymous book and published it as The Notebook, 2009, p. 29. No technical details about finger grips are mentioned.
It later hit the published page in Jean-Nicholas Ponsin's Nouvelle Magie Blanche Dévoilée, 1853, p. 37. This early description already has the modern finger grips in use, with the right hand's card both starting and ending between the right index finger and thumb.
Also see Bottom Change.