My heart is broken T_T
As for the real world time travel that I forgot about... well, let's put on our thinking caps about what's different between it and between G'raha's time travel. For starters, Alexander takes us back to a point where he had been summoned using the Enigma Codex. Rather than materializing beside a newly summoned version of himself, he assumes the same exact spacetime as his earlier self, meaning that either time travel as Alex does it has selfsame entities replace themselves when they travel or that summoning him merely calls him to a point in time, rather than creating him out of a vast quantity of aether.
Obviously it doesn't replace people, though Alexander did stand in for himself. This travel was also brief, did not try to change events, though that was the reason given from Roundrox as to why she manipulated Alexander to travel back to then. In G'raha's case he goes back in time with the intent to change history, and to stay in the past for as long as it takes. Yet, why does the intent matter or the duration? Well...
How the story views time is not that there are timelines. Quickthinx states that time is a, "flat round shape." A circle. This is how he's presented with time from Alexander as well, given that Alexander shows time in the control room as a spinning aetherial gear, which spins clockwise normally as seconds pass, but then counterclockwise when they go back in time. If that's the idea of how they want to pictorially represent time, then as long as you stay within the same, "time circle" then you don't create any paradoxes or changes. Even if we'd had the knowledge to try and act to help Mide or Dayan in the past, we weren't given the time to act. Alexander appears, the Goblins swoop and shoot, Alexander starts the vacuum, and Dayan pushes Mide out of the way and is sucked in. Then Alexander and every being associated with it are immediately flushed back to the present.
So what we have to consider aside from the briefness and personal intent is the fact that, Alexander's time travel as it is shown does not have Alexander change spatial coordinates. While I'm sure he can move spatially, we're never shown just how well he can move nor how fast nor if he can time travel to different spatial coordinates at all. This is a huge deal, because G'raha Tia Deluxe not only goes back in time, he leapfrogs from the Source to the First, and the First is at an unspecified spatial coordinates (with, apparently, a wibbly wobbly timezone flow of its own). In the bad future it doesn't even actually exist anymore, save as aetherial vestiges that have been rejoined into the Source. So by moving back in time to the First, the spatial jump took him and the Crystal Tower to the First in another, identical "time circle." Only, it was no longer identical once the tower boomtubed into being on The First.
So, basically, it was an accident that G'raha winds up in our, "time circle." The timelines were always separate.
Also, in regards to my cheekiness, I'm not living or dying by what I'm saying here. Just sharing my thoughts, and I'm trying to be lighthearted. The word deluxe comes to mind when I think of G'raha Tia because he makes us sandwiches. I often order deluxe sandwiches when I go to sandwich shops. He's a cat boy and a sage. Need I say more?