Bile Blight on Chronozoa
Your friend is right, the new copies aren't affected by Bile Blight.
The set of affected permanents / entities is determined at the resolution of the spell.
Of course it would have been a different story if this had been an enchantment along the lines of Engineered Plague

@tengfred already guided you towards an answer that has the exact ruling in his comment, but I've pasted it here for convenience as well.


  611.2c If a continuous effect generated by the resolution of a spell or ability modifies the characteristics or changes the controller of
  any objects, the set of objects it affects is determined when that
  continuous effect begins. After that point, the set won’t change.
  (Note that this works differently than a continuous effect from a
  static ability.) A continuous effect generated by the resolution of a
  spell or ability that doesn’t modify the characteristics or change the
  controller of any objects modifies the rules of the game, so it can
  affect objects that weren’t affected when that continuous effect
  began.