Sorry! When you mnetioned the girls will have no knowledge of their powers. I assumed that meant their involvement or knowledge of seed is the same. I can do a quick edit if I misunderstood.
Well, SEED isn't exactly secret, everyone probably knows that they're an organization to protect humanity from the Nephilim... but on the other hand someone particularly oblivious might not really make the connection.
Yeah, essentially because of Alexandra's backstory, she knows what SEED is (Since I assume SEED campaigned heavily for funding from America), she just doesn't have specifics about what she's doing, because her job description was 'You do what they tell you to do."