Even without the butterfly effect, there will be a split timeline. One world with the time traveler and one world without the time traveler. Although the rest of the world remains exactly the same, the mere presence of the time travel is enough to make them different. The first world must always remain in existence for there to have been an origin point for the time traveler.
I see, that all timelines already exists in the multiverse, and you are observing one of them. You can go to past and do whatever you wish, but the trick is, when you come back, you can choose do you want to come in a timeline with a different history.
I believe that if you go to your past, change something about it, put more energy and focus to a different timeline, you will be shifting in a future that has a different past as a way you have changed it. One fun thing is that you do not even need to go to past and change it, you can just simply shift in a paraller timeline that already has a different history