She is also the Duke's knight and swore an Oath to protect him. So there's that reason to help him. Of course if that woman the villainess is mean to you, you wouldn't go out of your way to save her, unless you are a submissive maso***** and into that, and if you are and cute let me give you my number. What are you going to do? Change the villainess personality to be nice somehow? Preemptively kill the female lead? She's a knight commoner she can't even talk to the villainess without her initiating conversation. Plus this is chapter one, if an opportunity arises she may try to save the villainess.
I love villainesses too but you are putting way too much on her at chapter 1 when she is shown not to be a powerful character in this world.