You have to ask the same question of Kanan and Ezra.
Remember Tarkin knows who they are and that they were Jedi.
Yet in ANH
Quote:
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Governor Tarkin: The Jedi are extinct, their fire has gone out of the universe. You, my friend, are all that's left of their religion.
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It makes sense that Tarkin didn't know about Kenobi or Yoda, they went into complete hiding. But Ezra and Kanan were on the front lines and Tarkin knew they were jedi.
The other question is what to do with Thrawn, he's become such a larger then life character, yet we don't see him in any Star Wars movies, I would expect that he has an Oh Crap moment as his ship blows up around him.