Is washing the roots of the hair with water and running fingers through them, as mentioned in the ghusl for janabah, done during wudu' or after its completion?

The sentence in question, "Then he would put his fingers in the water and run them through the roots of his hair," is found in the authentic hadith (definition) narrated by Aisha regarding the Prophet's description of ghusl (definition) (ritual bath) after major ritual impurity (janabah (definition)).

The apparent meaning of the hadith is that the hair should be run through after the complete ablution (wudu') for prayer, because the particle "then" implies sequence. This running through is done after completing the wudu', which is at the beginning of the ghusl and is commendable (mustahabb), as wudu' is a separate sunnah (definition) within the ghusl. And Allah knows best.