Sure your take on Alexander.
I look at it from a butterfly effect stand point. Every time a jump was made to alter history the previous past to that point could be describe as little more that a dream or a delusion for anyone who didn't do the time jump.
Its a machine and it thinks in calculations and it still needs to get the data from somewhere.
Plus instead of make a heap of jumps and through try a failure like in butterfly effect, it calculated the best point to stop it all and jumped to it.
It went straight to the start of time travel and said "I hate you" to Quickthinx Allthoughts lol
That one time was in this sequence of events.
Alexander time jumped in from where ever in time you feel it was to this moment to stop time travel.
I feel it jumped from the "dreamed" history lost after stopping time travel here
Not even a slide but more a BOOM
Out comes and Consequence are meaningless
Things yet to happen in the "past" in its future expansions wont haven taken effect in the "future"'s past form the start.
It has stunted any farther story telling in the "past"
However what your suggesting the isn't time travel because they never join .
You've been fooled into thinking its time travel but they aren't connected by time. What you have here is dimensional travel where one dimension looks like it might be the future of the other but it is not the case because changes made in the other past like dimension don't have an effect on the future dimension, they are separate dimensions .