The pdf covers it. The points move to the negative x region, thus the LT(2+h) point is closer to the origin, and to the right of LT(2) and thus it gets hit first.Therefore, time proceeded backward under the rules of SR.
Now, are you going to address this factual SR logic?
There is no contradiction, no problem, no issue with function maps, nothing. Under a sufficiently large boost in the x direction the 2 points at x=2 and x=2+h are shifted to the left so much that their x' values become quite negative. The LT(2+h) is then closer to the origin, where the light sphere spreads from, and so it gets hit first.
It's shown in the picture in the pdf. The LT slides the points from the right to the left and in the new frame the sphere spreading from the origin hits LT(2+h) first. Where is the problem? You accept my algebra and you've previously accepted my picture. Thus you accept there is nothing wrong. Therefore you accept your initial claim was mistaken. The thread is done.