Hey, it's a long story.
Before we start, it's worth noting that books and people can contradict each other. A simple example would be http://www.imperial-library.info/dfbooks/b084_betony_daggerfall.shtml and http://www.imperial-library.info/dfbooks/b083_betony_sentinel.shtml but it comes in forms.
It's less obvious in http://www.imperial-library.info/mwbooks/monomyth.shtml and the descriptions in http://www.imperial-library.info/mwbooks/varietiesoffaith.shtml but the same principle applies. Different views on the event of creation.
The same goes for the Amulet of Kings.
http://www.imperial-library.info/obbooks/amulet_kings.shtml and the http://www.imperial-library.info/obbooks/trials_st_alessia.shtml both describe the event in which Akatosh gives the Amulet of Alessia.
There are three claims here that are worth examining. The Amulet of Kings was made by Akatosh and when worn by the right person would protected the Empire against Oblivion.
The right peopleThe Septims obviously are the right people. They have been wearing the Amulet after all. Though not all Emperors have been direct descendants of Tiber Septim. Katariah for example was a Dunmer. There have been adoptions, sometimes a branch ended in a dead end in which the Throne passed onto a cousin. Comes to mind that after the second Emperor, the Septims aren't even descendant from Tiber Septim any more
1.
So the claim of the Amulet of Kings doesn't hold.
The Trials claim that any descendant of Alessia can wear the Amulet. Considering Alessia lived some four thousand years ago, there will be many people who can. It's plausible but puts the Story of Oblivion on a very shaky ground. If almost anybody could wear the Amulet, there would be no reason to go and find Martin.
You pore over your dusty tomes of lore. You study ancient genealogies and bloodlines. Look you to blood for truth? There is truth in blood, but it is not the truth that you seek! - http://www.imperial-library.info/tsoo/kotn01a.shtml
So it might be best to discard any and all blood relations as a factor altogether. Why some people can, and others (you) can't. Isn't clear. One explanation suggests that to wear the Amulet you need to have the proper role.
Protects against OblivionHalfway through the first Era and the whole of the Second Era there had been no Emperor with the Amulet of Kings on the throne. During this time there was no Invasion from Oblivon. If the Dragon Fires keep the Daedra out, then they are not the only thing which keep the Daedra out.
These other structures are explained in the http://www.imperial-library.info/obscure_text/nu-hatta_nu-mantia.shtml.
Amulet made by AkatoshThere is very little known about the Amulet of Kings. Before Oblivion we knew this:
1E 266 The Apotheosis of Alessia. The earlier record says that Shezarr, the missing sibling god of the Eight Divines, arrives at the White Gold Tower in the Imperial City and transforms the dying Alessia into the first of the Cyrodiilic saints. Thus Empress Alessia becomes the first gem in the Amulet of Kings. - http://www.imperial-library.info/history/1.shtml
Reman (The Cyrodiil) Culture god-hero of the Second Empire, Reman was the greatest hero of the Akaviri Trouble. Indeed, he convinced the invaders to help him build his own empire, and conquered all of Tamriel except for Morrowind. He instituted the rites of becoming Emperor, which included the creation of the Amulet of Kings, a soulgem of immense power. His Dynasty was ended by the Dunmeri Morag Tong at the end of the first era. Also called the Worldly God. - http://www.imperial-library.info/mwbooks/varietiesoffaith.shtml
And with the Nu-Mantia Intercept we know that the Amulet of Kings was made by the Ayleid as focal point for the reallity shaping power of the White-Gold Tower.
The (re)creation of the Amulet by Reman is explained better in http://www.imperial-library.info/obbooks/remanada.shtml where Reman was supposedly born from Hrols intent to reform Cyrodiil in the way of the Dragon Fires.
The supposed creation by Akatosh or Shezarr finds origins in the confusion around Alessias apotheosis were both were present.
With all that, that the actual origin from the Amulet of Kings as Ayleid being overlooked is understandable as embellishment.