An axion of Surak is, " the needs of the many outweigh the needs of the one". That alone should guide Spock to try and save Vulcan.
This is another universe, in which t does not follow that Hobus will destroy Romulus and Remus? Does time agent Daniels and coworkers patrol any timelines but the prime one?
Finally, in the TOS era, did not every ship have its own "logo", which change before ST vI?
An image in my catalogue has a Kelvin uniform with the Enterprise chevon on it as well as on cadet uniforms.Another piece of evidence that the JJverse did not come from the Prime one.