To be honest, I feel like firelink shrine is more like the Nexus from Demon Souls, or the Dream from bloodborne. A place disconnected from "reality", but something that can be entered under special conditions.
The untended graves are the "real" thing. A dead flame, slowly spreading the abyss, just like Lothric and Lorian wanted. And it does spread, as seen by the area in front of oceiros. It even spreads as far as into the firelink shrine, when it spreads out of gundyr.
Stuff happening affects the NPC's in the shrine. The handmaiden recognizes us, because she is still linked to her "real" self in the untended graves, but the "spell", probably that of filianore, prevents her from realizing that she isn't the real handmaiden. After all, she respawns, while the one in UG does not. Same thing goes for the firekeeper, who is already dead in the UG. And if you give her the eyes, she comes to realize, that the Firelink shrine she is in, is not real - that she herself isn't real. Other characters can enter and leave the shrine, but they all are the real deal and not involved in the shrines "spell", that copied the handmaiden, the firekeeper and Andre.
Also, there is no character that joins the firelink shrine unless he made contact with you, despite Leonhardt, who is a notorious invader.
It's not a question of past, future or present, it's a question of real or not. A theme all dark Souls games inhertied at some point:
Dark Souls one had Gwyndolins spell on Anor Londo, to keep up the illusion of everything being fine.
Dark Souls 2 had Drangleic being entered through a weird maelstrom.
Dark Souls 3 has Filianore, te firelink shrine, and possibly the arch dragons peak, wich we enter much like we enter the memories in Dark Souls 2.
The only thing unclear to me is, who created the alternate firelink shrine. If it was Filianore, then how far did her spell reach? Was it only the ringed City? Firelink shrine? The whole game?
We find her hidden behind not one, not two, but three obstacles: Either inside the painted world or the Kiln of the first flame. Then in dreg heap. And after that, in the ringed city. Places normally unreachable, if not for the ashen one who linked gathered the lord souls.
Maybe she created one Nexus to protect herself (ringed city), and another one to protect the ashen one (firelink shrine).