All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
The narration which we came across in this regard is reported by Imaam Muslim and others . However, we have not come across the part, "Then he would stand to perform the supererogatory prayer," in any version of the narration. It might be that this addition was added by the scholars who explained this narration. For example, Al-Munaawi
said when interpreting the narration, "When he, sallallaahu ‘alayhi wa sallam , used to conclude the prayer by saying Salaam, he, sallallaahu ‘alayhi wa sallam, would not remain sitting, meaning between the obligatory prayer and the supererogatory prayer." Al-Baydhaawi
also pointed to this saying, “This (not sitting) applies to the prayers after which supererogatory prayers are performed, but not to prayers after which no supererogatory prayers are performed.”
The Hanafi School of jurisprudence uses the narration as evidence for delaying the legislated mentionnig of Allaah and supplication after the obligatory prayer until a person would perform his supererogatory prayer, and many of their scholars stated this, such as Al-Kamaal Ibn Al-Humaam . However, the majority of the scholars
differed in their view with the Hanafi scholars
and they interpreted the narration to mean that the Imaam should quickly turn towards the people he had led in prayer (after saying the mention of Allaah reported in the narration in your question).
Allaah Knows best.