What is true here? Is this simply artistic license to be vague for the player? Did the Divine actually die in the explosion and that was really the spirit the entire time? If that's the case, then why did we see the spirit as the real Justinia in the memory sequence?
Perhaps one of these things is true, or perhaps neither, or both. The Fade is a mysterious place where anything could be true.
LOL! Okay, but seriously now. The anchor is gained after the explosion. That is, if Trespasser is correct (and it possibly isn't because it's so bad). Solas states that he intended for Corypheus to unlock the orb, for the resulting explosion to kill him, and then he would reclaim the orb. He would then enter the Fade using the mark.
So according to Solas, simply touching the orb would not bestow the anchor. The explosion would not bestow it either, as that was meant to kill whoever unlocked it.
So, that leaves after the explosion as the only time the Herald could have obtained it.
Related to this is your question about Justinia. The one we saw in the memories and in the Fade was not Justinia. Rather, that was the spirit that was watching over her. Justinia died in the explosion like everyone else. The spirit protected the Herald from the explosion. That is why the Herald survived it. After the explosion ended, the mark then transferred to the Herald either automatically or with the spirit's help.
From that point, the Herald physically moved through the Fade, ran from the Nightmare, and so forth.
As for the memories, the scene we see at the start of the game is the true memory. Parts of that memory were lost because the spirit that saved you was projecting an image of Justinia to make you feel safe and trusting. You lost parts of the memory because you were frightened and the Nightmare fed on your fears. So in effect, you were already being attacked by the Nightmare and your memories were being consumed. The spirit was trying to help you escape the Nightmare. During this tug of war between the Nightmare and the spirit small bits of the truth were perceived by you, which is why you see the spirit as it was during the intro scenes. But your recovered memories are altered by the spirit.
So the false memories really did happen, you just forgot them because the Nightmare stole them from you. But it still happened. The spirit impersonated Justinia in order to get you to follow her. That's also why "Justinia" let go, because she couldn't follow you anyway and she remained to keep doing battle with the Nightmare.
The real questions are, why did you go to the Fade after the explosion, and why did the orb stay in the real world? Perhaps the orb itself was a gateway of sorts along with the anchor, but I suppose anything is possible.