For a comprehensive treatment of the Succah-Shemini Atzeres issue, please read the chapter on this topic in “???? ?????? ????”
by Professor Eric Zimmer of Bar-Ilan University. In it you will see that the confusion that exists today has existed since the times of the Geonim and maybe even since the times of the Amoraim. One of the Rishonim used to eat in the house on Leil Shemini Atzeres, only to return to the succah the following day!