The closest I come is he was on one end of the Enantiomorph with Akatosh at the other... but yeah you're right. Chim El-adabal was the tool of the Empire's symbolic dominance over Tamriel (being the stone of White-Gold). Tiber may have wielded it, but Talos was a stand-in for Shezzar/Lorkhan/Man's accomplishments, not his right of dominance.