I don’t think I’ve ever directly posted this here, but here it is at least for reference: this is from the canon prelude comic to Age of Ultron, explaining why the twins volunteered. While I don’t blame anyone for not reading this comic or not knowing what happens in it, canonically, the twins thought they were volunteering with SHIELD.

There’s some problem with the logic of the twins’ motivation that stems from the writing one way or another, but in the comic, HYDRA is very aware the twins wouldn’t be cool working with them if they knew.