There's no "magical gateway" and time isn't getting unhinged, it's just lazy writing. The way the book was split, Brandon and Maria made their job to keep every straight very difficult. It seems they have not succeeded everywhere not to make mistakes.

As for Tam, there isn't any confusion or mistake, except for the fact at the end of TOM he's back with Perrin, and we're given absolutely no explanation how and when this happened. Perrin's thoughts at the end don't indicate any recent encounter with Rand (or discussion of Rand's plans and news with Tam) since the epiphany, and Tam didn't return to Perrin before he left Ghealdan, so it's quite unclear when Rand sent Tam back to Perrin... or why he didn't pass messages to Perrin through Tam when he did. Perhaps this is a mistake, and Tam shouldn't have been mentionned has having returned (like Sulin, in TGS who appeared by mistake in Rand's storyline) Brandon will have to clear this out.

Brandon had to juggle with different timelines, and didn't put enough pointers in each one to remind the readers of this as the book progressed, the way Jordan would have done in earlier books in the same situation (in COT, for example). There are pointers, just a bit too far apart (some are only in TGS) for the average readers (forum people, who've discussed the timeline a lot in the past, were not confused by this - we all remembered Perrin was at least a month behind)

In TGS shortly after Malden, Perrin saw Rand still in Tear at the manor, before he captured Semirhage.

Toward the end of TGS, Rand at Nynaeve's request located Perrin with the colour swirls. He was on the Jehannah Road, near the statue, with Galad (we now know Rand saw the trial scene).

Cadsuane came or sent for Tam a short while after the trial. A few days later, Perrin saw Rand on DM.

Tam was seen in Tear at the beginning of the book, because Rand's storyline in TOM is set after his epiphany. Loosely speaking, Perrin was already in the Forging scene/battle with Mesaana around this time, and Tam had left him.

The same thing happened with Elayne (but this was more confusing, and many people didn't even notice it...). She was on a different timeline in her scene with Egwene (post reunification) than she was in her scenes with Mat. That's why she never refers to the Seanchan attack or the reunification of the Tower in her scenes with Mat, or why she didn't think of the BA purge when she went to the dungeons (and why the BA were still there, and Egwene had not sent for them and executed them). It had not happened yet, it was weeks before. When Elayne meets Egwene toward the beginning of the book, and the purge is brought up, the scene when the BA escape from Elayne is already a while in the past.

When Joline and co. left for the Tower, the reunification was still upcoming, and the rumour it had happened was wrong. When they arrived to TV, a few weeks later (2, if I remember it right), it had taken place in the meantime.

The timelines are now a bit blurry and vague, that's all - it will be a headache to narrow it down to specific dates and make everything fit (and mistakes will probably surface).

We know Brandon has shifted things around (he modified a bit the order certain events would happen, because of the book split), and Mat's story line seems made of chapters written by RJ (Ghenjei for sure, and I think the Seven-Stripped Lass too) and others by Brandon, and not all the inconsistencies were spotted and smoothed out. Perrin forged his Hammer shortly after Rand's epiphany. He moves to Andor days later, so quite a bit ahead of the meeting with Rand (set a month after his epiphany). What doesn't fit is that Perrin and Egwene fight Mesaana latet than that, shortly before the big meeting with Rand will take place. Elayne too has a blurry timeline, taking the Sun Throne shortly before the reunion.

The storyline that will require a lot of research to map out is Mat's. In TGS, he came to Caemlyn on a certain date, 30 days before the end of TGS. He starts a few days after that in TOM. It seems he goes to Ghenjei around 30 days after his arrival. He is away when Verin's deadline lapses.

But this doesn't work. Mat meets Perrin in the first week after Rand's epiphany. A short while later, Perrin meets Elayne, and Mat has left for Ghenjei. So Mat has still not gone to Ghenjei days after the deadline of Verin has lapsed (we're already many days after her "30 days", but Mat doesn't acknowledge the delay has lapsed when it did... which would have been a good pointer... the sort Brandon failed to put in the book to help us...) We don't know how much time elapsed in the human world while Mat was at Ghenjei, and that's probably the only explanation: Mat entered it in the week after Rand's epiphany, and came out of there weeks later, very shortly before the meeting in the North. That's where Moiraine will show up to meet Rand (start theorizing right now about her crucial role at that meeting... she may be the one who reveals to Rand he musn't break the seals just yet, and why... or to bring the argument that will shatter all opposition from the WT and its alliance).

Elayne takes the Sun Throne shortly before the meeting in the North, and sends her new Cairhienin troops directly there. That means the attack on Caemlyn has not yet happened (it takes place while Mat is at Ghenjei). This means there's an ellipse of a few weeks in Elayne's storyline and Perrin's. We leave them not very long after Rand's epiphany, and we catch up with them weeks later, while on their way to the North. In the interim, Tam has seemingly returned to Perrin. The attack on Caemlyn takes place as everyone is going North. Only the Band is there. Elayne, Perrin etc. have left Caemlyn by then. Elayne has probably sent her Andorans north already, and taken the Kin with her so the Cairhienin can be sent North too (and to move her army/bodyguards of the Band etc.) The sisters at the BT might manage to escape and go to Tar Valon to raise the alarm, but there should be a delay. We don't know how much of the White Tower Egwene intends to bring to the meeting with Rand... if she decides to make a show and bring every last initiates, then it looks bad for Caemlyn especially if Moiraine convinces Mat not to go to Caemlyn but head straight for Rand in the north.. and if the BT gets involved. It looks likely Caemlyn will have fallen and be destroyed, or been turned in the Shadow's powerbase out of the Blight during the meeting in the North.

If Demandred is behind all this (as I still believe he is, there are new clues the BT is a part of his global army in TOM), then it will be worse than this: he will seize not only Caemlyn, but he will also move for Cairhien and maybe the Stone of Tear. That will secure Waygates for his Shadowspawn to move between the Shadow's powerbases south of the Blight, and at least two Portal Stones to send them elsewhere. That would pretty much leave only Tar Valon as the last great fortress of the Light.

If Demandred really has people near Roedran as well, he will use him as proxy as is his habit. It's obvious now he'd be useless against Andor, the Shadow has already taken care of that. So the obvious, if Demandred really has pawns near Roedran (I'm still not convinced) that the chaos he could create is by having the Murandians invade Altara. The Seanchan would delay their plans for the North to deal with this. They'll slaughter the Murandians in a short time, but not short enough. If Tuon moves her armies north as she plans, she too could lose her base of operations in the South early to the Shadow... As soon as she moves north en masse, Demandred could easily attack all her supply bases, destroy all her non-com bureaucrats, her supply camps and her lines of supply and communication... everything that makes the Seanchan armies so efficient... They can't live off the land, the land is almost dead.. they would have to rely on Rand, or Travel to their continent, or fight to the dead... But before it gets to that, another major catastophe is in the making: it sounds like Demandred's early strike (at Caemlyn for sure, and probably other cities) is timed to coincide with Rand's big meeting, and Tuon's arrival north is likely to happen at a similar time... this means the two big enemy factions in the Light are about to have all their forces facing one another, while the Shadow is making a surprise attack at its powerbases... Whoever will turn Tuon around: Egwene, Mat, Rand or others, it needs to happen soon or the whole forces of the Light will clash together.