This is the way I've seen it for 45 years.
And the bum was most likely to have died without affecting much of anything in his life after that point, so his death didn't butterfly effect anything else notable into the timeline. Although, I am totally fine with him being the original reason Edith was trying to cross the street at that moment. Time WANTS to happen..... oh wait, wrong show....

The Kelvinverse could have already existed, meaning red matter opened a door between Universes, which is honestly more likely, and which explains more of the changes easier, anyways. From a logical perspective, though, everything from Yesterday's Enterprise, City, even TVH suggest otherwise. I think the show Fringe handled the differences between timelines and universes quite ingeniously.