What is the ruling on one who has intercourse with his wife during the day while she is making up for missed fasts, thinking that the ruling on making up for missed fasts is the same as the ruling on voluntary fasting? And is there anything required of him for that?

Making up for missed Ramadan fasts is an obligatory fast that cannot be broken except for a legitimate Shar'i excuse. Once one begins to make it up, it becomes binding to complete it. This differs from a voluntary fast, which one is permitted to break. The expiation for intercourse (Kaffarat al-Jima') is only obligatory for intercourse that occurs during the daytime of Ramadan itself. Therefore, nothing is binding upon you. Rather, what is binding upon her is to make up that day again, along with repentance.