King of Tokyo (2016 version): Psychic Probe
According to Richard Garfield the game's designer, the timing of Psychic Probe interacting with cards such as Plot Twist, Stretchy, or Herd Culler is reactive - one player must commit to the use of their card, then the other must decide to use their card - there is no specific order in which these cards will always resolve and if neither player opts to use their card then the existing roll stands.

The clarification for this can be found here in the comments on one of Richards podcasts.

Obviously based on the date and content of the podcast, this was intended as a clarification for first edition, but unless the rules have changed significantly on any of the cards (which as far as I can see, they haven't) it would still apply for second edition.