Please pick a history book of your choice and read if Saad paid allegiance to Hazrat Ali or not. Saad was made governor by Hazrat Umar. By the time of Hazrat Ali he had retired and living in his famous house on the outskirts of Madina. As for allegiance, there were more like Abdullah ibne Umar, Usamah ibn Zayd, Muhammad ibn Maslamah who did not pay allegiance to Hazrat Ali.
I will give you a tradition from Sahih Muslim to look at which again interestingly involves Saad Ibne Abi Waqas!