in -LORE- its stated that the Septims can wear the Amulet because thats the pact. Alessia's Sister was a Septim and they are blood related, they are Hereditary and thats what allows them to wear the Amulet,each ruler dies and its soul goes into the Amulet. when you hear Dragonborn it IS symbolic for them because that is the nature of the Empire from the pact with Akatosh, Im not sure how many times this needs to be rrepeatedd, They don't Fus ro dah or have Dragon souls, Tiber was Shezzarine which is why he was so god awful strong he was several people at once he's special NOT because he has the soul of a Dragon, he didnt know Thu'um he learned it, made a college about it in the IC and was powerful enough BECUASE HE WAS SHEZZARINE to hear the Greybeards Talk, he also Achieved Chim and freaking changed the climate of the land.....
The lore is also from in-game sources, and thus is fallible.
Never read anything about Alessia's sister being a Septim, or her having any family at all, for that matter; got a source on that one?
Also, it's likely the emperors aren't fus ro dahing people simply because they didn't learn how, which even the Dragonborn need to do; it's not a common discipline outside of Skyrim.
And the college was in Markath Side, not the Imperial City.