The E-C going through the Rift IS the Original Timeline...
The change comes about when it doesn't go back right away to be destroyed and thus, impress the Klingon's.
But the delay it seems, is also a part of the original time line and the decades of war are just a blip in the grand shceme of things.
The real alteration is the change in Tasha's time line, which then begins to alter the original time line.
You have to think of time travel in terms of causality, not chronology.
In "Yesterday's Enterprise," as I recall, the Enterprise-C was in a battle with Romulans, and a spread of photon torpedoes opened a spatial rift causing the Enterprise-C to disappear. That happened in all timelines.
The torpedoes caused the rift, and the rift caused the ship to disappear. The disappearance of the ship caused the Klingon outpost to be destroyed, and that caused the Klingons to be at war with the Federation 20 years later. So far, this chain of causality in uninterrupted, and no alternate timelines are involved.
Then the Enterprise-D encounters the Enterprise-C emerging from the rift after 20 years, and is faced with the decision whether to send it back.
Guinan, who has lived for hundreds of years, and has previously met the alternate Picard in "Time's Arrow, Part II" and in the Nexus in "Star Trek Generations," realizes that this timeline and this Picard do not match the ones she remembers, so she tells Picard to send the ship back in time to alter the past.
Guinan's advice causes Picard to send Yar and the Enterprise-C back in time, and that travel into the past causes a new chain of events, where Yar is captured by the Romulans and has a half-Romulan daughter, and the Klingons do not go to war with the Federation, and Worf is a Starfleet officer.
So this is the timeline we see at the beginning and end of "Yesterday's Enterprise." Nothing in this "Lt. Worf" timeline caused the "Lt. Yar" timeline (unless you count Guinan's awareness of its existence). Rather, it was Picard's decision, during the war with the Klingons, that caused the Enterprise-C to go back in time and create a new timeline where Worf would join Starfleet and Yar would be killed by the tar monster.
(Conversely, there is no chain of events in the "Lt Worf" timeline that would have caused the "Lt. Yar" timeline to be created, so it cannot have been the original timeline. It was only the fact that the Enterprise-C returned from the original future, with Lt. Yar aboard, that caused history to be changed, and that change resulted in the timeline we have seen in every other TNG episode, with Lt. Worf on the Enterprise-D.)
So the disappearance of the Enterprise-C did not cause an alternate timeline, since that event would have happened the same way in all timelines. The only event that caused a change in history was the Enterprise-C returning to the past, which was caused by Picard's decision 20 years in the future.
Yes, before "Yesterday's Enterprise" aired, we had seen 60 other TNG episodes set in that new timeline, where future-Yar had already come back and had a half-Romulan daughter. But just because you saw this timeline first chronologically, and in fact the "Lt. Worf" timeline appeared at the beginning and the end of "Yesterday's Enterprise," that doesn't mean that anything in this timeline
caused the Klingon war in the "Lt. Yar" timeline.
The string of causality shows that the "Lt. Yar" timeline was the natural course of history, and only by sending the Enterprise-C back in time were any changes in the timeline created.
You just have to ask yourself, "What caused what to happen?" not, "What did I see happen first?"