This is your assumptions but the prophet himself has included the members of purified family ie Ahl albayat upto the last member ie 12 Imam Al-Mahdi. only 4 members were alive in the life of the prophet saww thus you can find 4 members under the cloak / kissa at the revelation of the verse of purification. The narrations about 12 caliphs / ameers / Imams/ successors  from Quresh are present in both sunnis and shia sources. Those 12 names include the first one is Imam Ali and the last  ie12