A common image in time travel stories is an image of all time, either as a line or a tree form. Take this image from Loki as an example:
So a time traveller's organisation, like the one for my story, has a way to look at the "normal timeline", the one muggles live in, so that they can insert themselves at any point and make any changes necessary. They know the beginning and the end of the normal timeline and can see it all at once, so it is like they are looking from atop it - like a 3D person looking at 2D Flatlanders. This suggests they are in a different temporal dimension of their own. That is further supported by the fact that there is a timeline that the time travellers experience; events take place in their office which follow each other causally, there's a start of the time travel agency and an end to it. They are just as bound to time as we are, they are just natively on a different temporal dimension and they have the technology to look at the normal timeline as a whole.
I have provided an illustration of my concept. The red flow of time (temporal dimension) is the "normal" one. On it is a timeline that changes over the course of the second temporal dimension. That means that at any given "moment", the red timeline starts at the start, ends at the end, and every event within it is causally related - or is it? I'll get back to that; but understand that it can't loop or branch, it's always a line. This timeline does constantly change as the blue time progresses; events move or change, the end may be expedited or delayed.
The blue time is the time of the time travellers. They exist natively to the blue timeline; they can see the red timeline from start to finish as it exists at that moment, and they of course keep records of what it used to look like. They can use that to make interventions, change events as they see fit, and add non-casuality to the red timeline. But the blue is causal; event 1 is followed by 2 and 3.
The blue time "interferes" with the red time passively, we call it quantum randomness. For every instance of a red timeline, the quantum dice were rolled in a specific way and that normally determined the order of events. When a time traveller visits the red timeline, they are manipulating quantum tunneling to materialise themselves at a place and time, seemingly out of thin air. Conservation of energy is still maintained in the red timeline however; they need to ensure those particles that form their body disappear somewhere else in the universe, or at least equivalent mass-energy.
This idea really scratched an itch I have for stories featuring multiple dimensions, but it brought one issue to light. Can't the time travellers take their timeline-viewing machine, go into the normal timeline, turn the machine on and view their own temporal dimension from start to finish? Wouldn't they be able to see their own lives and deaths and actions? That would make plot involving the time travellers impossible and meaningless.
One can come up with mundane reasons why the timeline-viewing-tech may not be physically transportable to the Muggle Earth, but those feel like cop-outs. How can I make the impossibility of seeing the blue flow of time from start to finish an inherent property of the system, rather than something arbitrary like tech restrictions?