In the film, she may have presumed there was some sort of reward on offer, but she definitely didn't know about the audition process - in fact, it's not until they're halfway to France that she finds out she's going to be vetted by the Empress's cousin and so agrees to learn about Anastasia's background - it's pretty clear from the start that her main goal is just to get to Paris, and she's playing along with whatever Vlad/Dimitri suggest in order to achieve this. It's a bit of a "don't ask, don't tell" situation, since both parties are using the other for their own gain.
But at one point Vlad confides in her that he was once a member of the Russian court, so - yeah, there is a chance that she believes he's the instigator of this plan, and is doing so out of loyalty to the royal family. "I might be Anastasia and these guys are hoping to get something out of it" is a very different assumption than "they know I'm not for real, and they're grooming me as part of an elaborate con."
In the musical, she knows about the auditions and the reward from the start (the song "Learn to Do It" is the like, the fourth song in the show) - in fact, the villain Gleb spells it out to her that she's either partaking in a cruel hoax, or her life is in danger from the Bolsheviks if it turns out she's really the lost princess. She and Dimitri also realize she's truly Anastasia at exactly the same time, which is well before they go to see the Empress, so there's no big explosion at the ballet when Anya thinks he's been gaslighting her into believing she's Anastasia/using her as a pawn in his scheme since they met.
Well, she was in love with Dimitri by that point, so it hurt more realizing the betrayal came from him. And Anya never gets the chance to yell at Vlad because he completely disappears from the story once Dimitri rejects the money!
I do agree though it's bizarre that Vlad gets off scot-free. He's a complicit and knowing partner in the scheme and is never held accountable for it. She does get the chance to call him out in the musical - though again, it doesn't have quite the same bite to it, as she fully knew what she was getting into.
If we could combine the best parts of the film (the love story, the redemption arc, the runaway train set-piece) with the best parts of the musical (no Rasputin, more historical accuracy, better characterization for Vlad, Sophie/Lily, Empress Marie) then we'd have a perfect movie.