I wonder how she calculated that she is over 4k years old. I mean, she doesn't know how long she sleept.
EDIT: Nevermind...
IMO she was born in time "between" empires, early Reman maybe, before he was proclaimed emperor by Akaviri ? Her father is wielding katana, however the sword could be obtained by him later.
And like you and others had mentioned, it is very possible she was born, lived, and was changed between the time of the Reman and Alyssian Empires.
If that
is the case, then she would still have no knowledge of an Empire as there wouldn't have been one during her lifetime or even before she slept.
However, in rebuttal, through out the Vampire side of the expansion you are given the opportunity to ask her questions to get more info on her and her family.
She mentions that after they were changed, they lived as a happy family for centuries before they started to grow apart and her father heard about the Prophecy. they dealt with it for more centuries until it was obvious that he was being driven mad by it (in her and her Mother's opinions).
Just the sheer amount of time she mentions spending as an awake Vampire (but still with no knowledge of a Cyrodiilic based Empire) leads me to believe that she lived, was "given" to Molag Bal, existed as a Vampire, and was shut away in the crypt well before either Empire existed.