In the season 1 finale of The Flash
Eddie Thawne shoots himself in order to erase the Reverse Flash, who is his descendant.
However, this does raise the question: Which Time Travel theory applies in The Flash?
The Reverse Flash's disappearance after Eddie shoots himself...
...would imply a single universe model, as changes in the past immediately affect the present. But according to this model...
...the Reverse Flash's disappearance should result in the timeline being reset (Barry's mother does not get killed in the first place, for instance).
But as, beside the disappearance, nothing like that happens, some form of multiverse or parallel universe is implied.
Wait! In such a multiverse, the disappearance would not take place at all, there would simply be a parallel timeline...
one in which Eddie did not kill himself, Reverse Flash is born and travels back, creating a parallel timeline in which Eddie kills himself and parallel Reverse Flash is not born, but the Reverse Flash version from the original timeline is still there.
So my question is: What rules does time travel follow in The Flash? Is there one Time Travel theory that would explain what we see in The Flash?
Note: I know there are some closely related questions out there. However, none of them deal with the events from the finale, and none of them address the general Time Travel theory in The Flash. IMHO
Edit: I quickly sketched the singleverse and multiverse theory applied to The Flash to illustrate my problem: