Muawiya eventually made a treaty with the Idumean confederation again in exchange for rule until his death in 680 but then his son Yazid killed the Alid Prince and broke away again which allowed ibn Al-Zubayr to take control of the Idumean confederation.
Overall, the archaeological record attests to these Idumean-style rulers in the area of the former Persian Empire from 651 to 692 a total of 21 years.
As they began to be conquered one by one by Abdul Malik, he adopted their style[https://www.coinarchives.com/w/lotviewer.php?LotID=4809920&AucID=5357&Lot=3&Val=930c083f565b53eb8418ef7d6abaa81e] and the Idumeans only began to be forced to accept the Anno Hegira from 692AD after Abdul Malik realized that Israel-centric uprisings would keep on coming back again and again if he did not eliminate the need for Mosaist-hierarchs.
Thus the Idumean rulers vanished from history. They might have been involved in the establishment of the Khazar Empire after that but otherwise seem to melt into the general Jewish community after that.
