It appeared in the following conversation.
A: It's about time you went home, don't you think?
B: You plan on saying "I'll take you" again, and coming with me, don't you? Well, I was going to go home even without you telling me. It's late.
A: Ah, I'll take you home.
B: Uwah,not even a twist.
B is a brother of "A"'s girlfriend.
A want to go out,but don't want his girlfriend knows where he exactly go.
So he make that excuse.
And he did it the other day.
I referred to a dictionary. The closest meaning is:
A twist in something is an unexpected and significant development.
But it seems that it doesn't match the context of the sentence well.