My theory that explains all the future nonsense.
1) Maggie is not from the future. She suffers from mental disorders, most likely brought upon by a childhood of sexual abuse by her father/stepfather. This father is the same father as Abigail. Which makes them sisters.
2) Maggie is the older sister, and ran away from home when she got older, and got into hard drugs, waking up in strange hotels with strange men, etc..... basically, completely out of her mind. Abigail doesn't recognize her older sister Maggie, because Abigail was too young when Maggie left, and the pedophile father didn't talk about her, out of anger that she ran away.
3) During one of these drug binges and psychosis episodes, the crazy white haired man, the guy in charge of the cult, he finds her, and he convinces Maggie that she is from the future, with that stupid "this tattoo means I'm a traveler" garbage. He infects her mind, and she is vulnerable and lost at this point in her life, so she actually believes it. She creates this new persona. She escapes her reality in her mind. Maggie is a victim of this cult, too.
4) The woman from the Department of Justice, is another cult member. I know this for several reasons, but mainly because of how paranoid she is. No FBI or DOJ staff goes into a hotel with a box of clothes, with a secret compartment of anti-espionage equipment. Police have nothing to hide. This woman obviously is hiding and running from law enforcement, or is simply another brainwashed cult member who has to make sure that her area is "safe" before she can receive her cult orders. She makes sure the room isn't bugged, and then opens up the instruction packet, with the instructions and pictures she will use.
5) The black woman, pretending to be DoJ, is there specifically to test Lorna and Peter.
6) Peter was targeted by the cult, and he didn't know it. His mother was part of a cult, so they had an idea of who he was and how vulnerable he might be. And he was in the perfect spot to grab Abigail for Maggie. We are never told how Peter found the cult. So, I would assume, the Cult made themselves available to Peter intentionally, and he took the bait unknowingly. Peter thought he was the reporter, tricking the Cult, but in reality the cult was tricking Peter from the start.
7) Maggie and Abigail both know the handshake, because it was taught to them by the same person. Perhaps the Mother? Abigail has no mother, in any of the scenes we see. Only a father, and a maid. So perhaps the mother died, after Maggie had run away already. But the mother taught both of them the secret handshake. And I think the mother died on 9/11. This is why Abigail is traumatized about terrorists and flaming buildings. Her mother died on September 11, 2001 in the terrorist attack.
8) Maggie wants to go back and save her little sister from her monster father.
9) Meanwhile, while all of this is happening, the real Cult masterminds, the white haired guy with glasses, he is probably planting all sorts of ideas in Maggie's head. Like, they should all be armed and ready for what's coming, etc... Perhaps they are all being secretly brainwashed to be a terrorist militia, or some other nefarious group, and even Maggie doesn't know it, because she is under the influence of the white haired man.
10) The whole arrest of Maggie is staged, for Peter's benefit. Peter is now convinced, and 100% brainwashed. And they successfully put a wedge inbetween Lorna and Peter, as their relationship will now end because Peter is upset at Lorna's betrayal, behind his back. The Cult has taken Peter.