Earlier quoted context omitted.
Nothing you just said contradicts my statement, which was, "there are frames of reference in which that information arrived at the destination before it left the origin." I suspect that you don't know anything at all about Special Relativity, in which case, there's not much more I can tell you except to go educate yourself.
Special Relativity only applies to cases where there is uniform relative movement in two or more inertial frames of reference. That is not the case with this theory - the relative movement is clearly not uniform and although I've not read the paper I'm certain that the time warp provides a non-inertial frame. TL;DR - ignore Special Relativity completely, General Relativity is the only thing that applies here.
Suppose we have guy A and guy B who have clocks. They're on spaceships which are both drifting away from each other (i.e. provide inertial frames) at speed c/root 2; at time t=0 they were in the same place. From SR it should be clear that in A's frame, his clock reads 100 at the same time as B's frame reads 50, while in B's frame, when his clock reads 50 A's clock reads 25. All this should be basic and obvious.
So suppose an event happens on A's ship at time tA=100, and he transmits this instantly (or sends a courier C on a warpship) to B at time tA=102, when B's clock reads tB=51.
From B's perspective, he's just received a message from A at time tB=51 (which is simultaneous with tA=25.5), which A is not going to send until tA=102 i.e. tB=404. Thus, B perceives a violation of causality.
(This becomes very obvious if B can send an insta-message back to A with the same technology; B sends it at time tB=54 which is simultaneous with tA=26, A receives it at tA=26, well before he sent the original message at tA=102)