'Urwa has narrated it on the authority of 'A'isha that when Messenger of Allah ﷺ took a bath because of sexual intercourse, he first washed his hands before dipping one of them into the basin, and then performed ablu- tion as is done for prayer. (Using translation from Muslim 316d)
أَنَّ رَسُولَ اللهِ ﷺ كَانَ إِذَا اغْتَسَلَ مِنَ الْجَنَابَةِ بَدَأَ فَغَسَلَ يَدَيْهِ مِنَ الْإِنَاءِ قَبْلَ أَنْ يُدْخِلَ يَدَهُ فِي الْإِنَاءِ ثُمَّ تَوَضَّأَ مِثْلَ وَضُوئِهِ لِلصَّلَاةِ