For those uninformed: The Butterfly Effect refers to a time travel theory in which one small change resultes in a wide spread (much like the wings of a butterfly) for many events along the timeline.
After giving it some thought I've determined that it's ALMOST impossible for Yu's time leap to have changed the timeline of events enough to produce the results we see in episode 11. I'm gonna lay this out bit by bit so bear with.
First of all we should create a brief list of events in both timelines.
Original (Pre-Time Leap) Timeline
•Yu goes to Student Counsel unaware of what will happen there and Ayumi's ability.
•Yu asks Ayumi to stay home to ensure she is safe, however she sneaks off to school anyways.
•Konishi causes Ayumi to panic, triggering her Collapse ability.
•Yu locks himself away in depression, turning away from everyone including Yuki.
•Agents show up at Yu's door step causing him to run to a faraway manga café.
•Yu begins a dark spiral in his life as he picks up poor eating habits, and begins picking fights with local gangs.
•As Yu is about to turn to drugs Mao reveals herself to have been watching him the whole time. She snap Yu back after feeding him Omurice made with the same homestyle pizza sauce recipe Ayumi used.
•Nao invites Yu to the ZHIEND concert.
•Yu encounters ZHIEND's vocalist Sara.
•Sara sings, causing an improvement in Kazuki's health
•Yu and Nao attend the concert.
•Yu passes out and flashes back to what was presumably Earth's original timeline.
•Yu wakes in hospital having regained memories from the past. (why memories from a timeline that has been retconed by Time Leap exist is unclear)
•Kumagami takes Yu and Nao to meet Shunsuke
•Yu uses Looting to take Shunuke's Time Leap ability, then Time Leaps to the day before Ayumi's death.
--END OF ORIGINAL TIMELINE--
New (Post-Time Leap) Timeline
•Yu goes to student counsel fully aware of what is to come.
•Yu easily convinces Nao that he is from the Future.
•Yu and friends plot to protect Ayumi.
•Yu sends Ayumi to school
•The Student Counsel attempts to keep an eye on Ayumi but their cover is blown.
•Yu Protects Ayumi from Konishi before Collapse is unleashed and uses Looting to confiscate the ability.
•Yu and Ayumi are confronted by Kumagami who takes them to Shunsuke.
•Shunsuke insists that Yu stay at the research facility until he is ability free as he is a big target.
•Kumagami detects an ability user and goes to inform the School Counsel.
•Kumagami's driver Furuki reveals that he secretly has a family and that they are being threatened.
•Furuki delivers Kumagami to terrorists with an interest in psychic abilities.
•The Terrorists torture Kumagami until he reveals everything he knows about Shunuske's operations.
•The Terrorists kidnap Nao.
•The Terrorists call Shunsuke demanding he send them the most powerful psychic, Yu.
•The Terrorists inform Shunsuke that they are aware of the Time Leap ability and should they notice anything suspect they will kill Nao and Kumagami.
•Shunsuke reveals his plan to only use Time Leap to return to this time to Yu who panics and almost unleashes Collapse.
•Furuki escorts Yu to the Terrorists who in turn give him keys to the condo Furuki's family is being held in.
•Yu uses Plunge to control the terrorist and his translator discovering they are unarmed.
•A mysterious ability user emerges from a dark hall and attacks Yu.
•The mysterious ability user slashes out Yu's right eye disabling the Time Leap ability.
•The mysterious girl continues to attack Yu who attempts to fight back with Telekinesis.
•Eventually the fighting results in Collapse being unleashed.
•Yu uses Telekinetic to protect himself from the falling rubble.
•Kumagami is killed shielding Nao from falling rubble.
--END OF NEW TIMELINE AS OF EPISODE 11--
Now that we have our list of events we should give them a general time frame so that we can try to piece together when things should have happened.
Yu is shown to have spent several days locked in his house alone. He is then shown to have spend a few more on the faraway streets. The ZHEIND arc takes about 3 or 4 days.
When Kumagami approaches Yu and Ayumi it appears to be the same day as the collapse incident. Although it is unclear how long is spent in the research facility it seems reasonable for it to have been around a day or two. It is sunset when Shunsuke approaches the wreckage of the warehouse.
Now we must look at the two timelines together and look and events that presumably happened the same way, and those that have changed.
In terms of things that still happened the way they did originally the only thing I can think of as being probable is that Kumagami still revived info about the ability user he detected, but since Nao was watching Yu, student counsel most likely didn't meet and the ability user was left to freely explore their powers on their own. We know that Kumagami did not get kidnapped in the Original Timeline since when he meets Yu in the hospital there are no signs of his torture whatsoever, and given the consequences of the kidnapping in the New Timeline he would certainly have been tortured had he been captured in the Original Timeline. At this point in the Original Timeline Yu is most likely still at home sulking, so beyond this point we don't have the info to determine if any more events line up.
Now that we have both timelines in relation to one another we have to ask why didn't the outcome of the New Timeline also occur in the Original Timeline.
It is heavily implied by the Terrorists that they have been watching Shunsuke and Co. for some time now, and even that they have Furuki's family under their thumb for a while now. It is beyond safe to assume that they must have been acting long before the timeline split, so what made them change their plan in the Original Timeline? From an outsider perspective both timelines so far as Shunsuke's work, and Yu's lives are very much the same. Yu would have stopped attending school (although for a much shorter period by this point), and Shunsuke would have continued work, so let's try and discover what would be visibly different in both universes. Ultimately two things come to mind, the middle school building is still standing, and from what we are shown it appears that Nao is continuing life as normal up until her kidnapping instead of watching Yu.
When it comes down to determining which of these two events lead to the attack it really is a no brainer. The events of Nao's life are inconsequential as the Terrorists are unaware of her existence until Kumagami revealed her identity in the New Timeline. The only thing that could possibly have raised any red flags with the Terrorists would have been the collapsing of the Middle School building. The next question that popped into my head is why would this event cause the Terrorists to back off, surely this wouldn't surprise them, they are after the most powerful psychic after all. The terrorists would have undoubtedly been aware that an ability user's power would have been capable of leveling a building, and if anything would have gained even more interest from the group. But what if it wasn't the event of the collapse itself and instead what the event entailed.
What I say from here on in is complete THEORY and CONJECTURE, I may very well be wrong on this front who knows. What if Ayumi wasn't the only one who died because of Collapse? It's all but impossible to think that should a whole multi story building with at least a couple hundred occupants could fall to the ground and the death be a single girl at the epicenter of the event. So far as I see the only way for the timeline to split so dramatically is for someone else to have died. There are actually a few candidates for who our second victim may be; it could have been a high terrorist operative, or even the terrorist leader running some reconnaissance himself this would have at the very least delayed their plans by a considerable amount of time, but I think the most likely candidate for the second victim is none other than Furuki himself! Although I can't think of any specific reasons for Furuki to be at the Middle School, it's not to terribly surprising that he could be there after all he worked from Shunsuke, the owner of the school, and must have been somewhat close to him at that as indicated when Shunsuke revealed that he was aware that he had a family as is against company policy, but that he had made a special exception. Should Furuki had died the Terrorists would have lost any hold they had on Shunsuke's company and their entire plan to learn about psychics would have completely fell apart sending them back to square one. Sure it's possible that they might have come back eventually but it definitely would have been a long time before they would be ready to attack again, many even years.
That's about all I have to say on this series use of bitterly effect and my thought's on the series implication of it. I want to know your thoughts, so be sure to share them