The Amulet of King's is supposed to hold the soul of every Emperor of Cyrodiil, we even hear that through the Amulet one could speak to the souls of past Emperors and the Council and current Emperors often consolted them for aid and advice.

That being said, we know the AoK was a soul gem, one of great power obviously if it was able to hold not only multiple souls, but the souls of 'Dragonborn' as well. My question is, has this always been a function of the AoK, or did this only come along after Remen instituted the rites via the Dragonfires? would that include Alssea, the Remens and the Septims?

If it truely does hold the souls of past Emperors, then it may have further implications that might make us question a few things already present in lore.

The Amulet of Kings does hold the souls of Emperors from before the rise of Reman, including Empress Hestra from the first century of the second millennium of the 1st Era. I would speculate that Alessia, the Remans, and the Septims are all contained within it.

As I recall, it says in The Amulet of Kings that she made up the first stone of the Amulet. Assuming that is correct, then I too would speculate that her soul would be contained within as well. However, we know from Skyrim, souls within gems are not able to act outside those gems and are in effect, traqed indefinitly until freed.

Malyn Varen in Skyrim for instance must rely on predetermined preperations from his students in order to get more souls from the outside world to fill Azura's Star. This leads me to wonder, had Alessia been indeed traqed inside the Amulet of Kings, how is it that her spirit was able to come lead King Hrol through the mud-slingy boogy to give birth to Remen? at that, how was Murkati seeing her spirit?