Maybe because she has the RI Library in her DNA?
I did see the date she chose (2032) was after Conner was injured (2028). I'm missing something as I would expect Conner to avoid his injury by "killing the dog" in the new stub (or will Burton and Connor also have memories of the other stub??).
2032 was her "present." By opening a new stub at the present, NeoFlynn, NeoBurton, and NeoConner will all have all their memories (since the moment of diversion between the two stubs is "now"), and NeoFlynn can pick up where Flynn left off when she died. If she had picked an earlier date, there would be no way for NeoFlynn to go after Cherise, because NeoFlynn would never have gone to the future and wouldn't know anything about the stubs, etc.
And yes, they will all "have memories" of the old stub, since the old stub up til "now" will be the shared past of both stubs. But Burton and Conner will simply go on with their lives after Flynn's death; presumably, their access to the future will be cut off (one would think they'd be killed because they know too much, but I guess that's not where the writers are going with all this). NeoFlynn, NeoBurton, and NeoConner will effectively be the characters we've known all along.