No idea what Omegaverse is but just to be sure: so the alpha smell was actually from her sister? She misinterpreted her feelings?
It is entirely possible that she's interpreting the scent that way because they're related. And I do not think she misunderstood her feelings. I think she very much understands she has feelings for the president. But she is shocked to realize that her biology desires the president's older sister.
I look at it as being sexually attracted to someone versus being emotionally attracted to someone. They're two very distinct things. And within omegaverse the trope often overlooks this, assuming that your physical attraction and emotional attraction will line up all the time. In this case, it is not lining up, but she doesn't seem put off too much, since it looks like she's already made up her mind about being with the president. If this keeps going she'll probably just find it difficult to ignore the president's older sister. (And who knows yet how the older sister will respond).