I thought of a different explanation for the Blaze split in the Sonic timeline. Don't worry, it doesn't involve made up characters or fan fictions this time. What if Solaris (or Iblis, the half form of Solaris) messed with dimensions and brought Blaze and Eggman Nega to the future without clear memories of who they were. Then, when the timeline got erased, Eggman Nega, remained in another dimension and in the future, due to the imperfect mending of the time paradox. The future Eggman Nega, without clear memory, assumed he was a descendant of Eggman, and thus Rivals kicks in.