The Potentate Versuda Shae was Chancellor to the then Emperor and after arranging the permanent absence of the entire royalk family at the hands of said Emperor the Potentate / Chancellor then arranged the demise of the Emperor himself and thus remained chancellor as the sole power until (in the interests of maintaining stability) he finally, 'reluctantly' accepted the Imperial Seat.
Of course he did not live forever ... so either immorrtal indicates there are incredibly long-lived Tsaesci - or there are certain other limitations to their potential immortality. Or the Tsaesci Emperor was not Tsaesci ...
Otherwise, could the 'humans' on the other continent have been assimilated into the Tsaesci bloodlines or svcked to death by them?
Also, just thinking that the 'true' Tsaesci might be a faction within that far-off race that indeed was immortal and that the entire race then took the name of that faction.
Unless more Lore is presented such 'how it works in practice' questions are likely to remain unanswered.