Was the custom of covering Kaaba in black cloth adopted during the Fatimid era?

Question

This answer to Why is the Kaaba covered in black cloth? states that the black cloth for Kaaba a tradition which is continued to-date was adopted by the Fatimids.

Is that correct?

Answer 1

No; after the Fatmids.

Wikipedia to the rescue

Later on, Al-Nasir the Abbasid draped the Kaaba with green, both Al Nasir and Al-Ma'mun disagreed on the frequent color changes and switched to black, and black it remains to this day. Kiswah

Al Nasir ruled from 1180; the Fatmids appear to be 909 to 1171.