Sayyidah Aishah (may Allah be pleased with her) says: When the Messenger of Allah (peace and blessings be upon him) intended to take the ritual bath for janabah (major impurity), he would wash his hands before putting them into the vessel, then wash his private part, then perform ablution as for prayer, then soak his hair with water, then pour three handfuls of water over his head.
Imam al-Shafi'i (may Allah have mercy on him) narrates it with his chain from Hisham, and in this hadith it says: he would wash his hand before putting it into the vessel.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الطهارة / 830