I have a similar take on the 'illusion of time'. One can get a sense of it when playing chess against a chess engine.Perhaps an analogy would be walking a path (3D) versus looking at a map (higher existence). Only that the map has an additional dimension that makes the 2D map dynamic as opposed to "fixed".
The average player only can see the current move and, at best, ascribe some probabilities to a few moves ahead. Basically he is stuck in the present, all he can see is the present move (and a blurry short term future).
For the chess engine things are very different. For a given position it can 'see' all the possible moves and the ultimate outcome (victory, loss, draw) of each scenario.
Thus, for the chess engine, playing chess is not an iterative process, i.e. choosing what seems to be the best move in the present position, but rather it is about choosing the moves that leads to the set of scenario with the highest probability of victory.
In this sense, the chess engine is beyond linear time. It has transcended the limitations of the illusion of linear time. It can see all the possible 'futures' and their probabilities.
Chess games are sometimes modelized by what is called 'chess tree of analysis':
In the picture above, the player's 'present' is at move 5 (see red dot). All he can see is the four previous moves (that's the 'past', see the 4 red lines) and the present (red dot), he can also imagine a few of the probable short-term 'futures' (transparent red ellipses). The players is very much in the linear time, his perception is limited to the part of tree that is highlighted in red.
Meanwhile, in any position, the chess engine can see the whole tree: all the moves that led to the 'present' position and all the 'future' scenarios that stem from the 'present' position. This doesn't mean that the chess engine doesn't make decision. It does, but those decisions are not constrained by a linear perception of time.
This might explain why 4D STS are busy moving back in the 'past' to modify timelines. Basically this is what a chess player does when he plays against a chess engine: when the players sees he will lose the game (all the remaining possible scenarios lead to a loss) he can cancel several past moves (moving back in the 'past' to modify the timeline) and replace his wrong moves with better moves that preserve in the 'present' his probabilities to win.
When a player does that, he's not constrained by linear time any more, he moves back and forth the timelines, exploring them and choosing which one matches his victory goal the best.