This Double Turnover is done by applying upward pressure with the tip of the forefinger to the outer end of the top two cards, bowing their center upward. Pressure is then released by either the fingertips or the thumb, which causes the double to spring up and over onto the deck. According to Rafael Benatar, a group of Spanish magicians saw Fred Kaps do this flourish Double Turnover at the Spanish National Convention in Cuenca in 1977. Sometime after the convention, Kaps stopped in Madrid and taught it to Camilo Vázquez, who was the first to use it in Spain. The first published description seems to be in José Carroll's Fifty-two Lovers Vol. 1, 1988, p. 61. Carroll confirms the source as being Kaps in Cuenca. Kaps released with the thumb, causing the double to flip over clockwise. Carroll releases with the fingertips, making the double flip counterclockwise.
The springing turnover technique, done with just one card, was developed by Eddie Fechter and used as a flashy revelation of the top card. See “Spring Card Revelation” in Jerry Mentzer's book on Eddie Fechter, "Magician Nitely", 1974, p. 121.
An earlier related flourish appeared under the title of “15. Card Jumps Out of Pack” in Stanyon's Magic, Vol. 13 No. 1, Oct. 1912, p. 4, without attribution. In it, the top card is raised at one side and squeezed between the tips of the fingers and thumb to bow it concavely until it springs free and into the air.