TT #392 · Parashas Shoftim · Seventh Aliyah · Passuk 21:08
Atone for Your people Yisrael whom You have redeemed, O Eternal, and do not place innocent blood in the midst of Your people Yisrael. And the blood shall be atoned for them.
Torah Temimah points to Sotah 47a.
TT lemma: וְנִכַּפֵּר לָהֶם הַדָּם.
English: ‘And the blood shall be atoned for them’ – immediately.
Derash on the timing of atonement (Bavli) — once the process is finished the kapparah is present.
As soon as the rite and the declarations are complete, the blood is atoned for the people.