The tension has been there for a while, but this update it has spilled over such that other girls have started to notice. In the new main event "World of Lines":
My interpretation of this is that she is hesitating because she is lying. She DOES know a lot about him, through Niki and through Rin's revelations. Otoha's suspicion of Sensei comes from how Niki has portrayed him, the man who broke her heart. From Otoha event "Japanese Summer (Double Suicide)",
From that event onward, Otoha becomes gradually more suspicious of Sensei's intentions, but their "big brother-little sister" bond still persists. They even get to the point of flirting in the Otoha event "Breathing in Unison". Where Otoha REALLY becomes suspicious is when she realizes
Sensei is also with Chika, when Rin blurts it out in Rin event "Ever Fallen in Love".
What "she knows" that she is withholding from Touka and Imani is that Sensei is fucking a student, Chika. She also knows he is capable of cruelly abandoning someone who loves him (Niki). And yet, her feeling isn't disgust, otherwise she would just blurt out what is happening under that pressure. I don't think the reason she keeps the secret is for Rin, either, as she isn't portrayed as a selfless person like Futaba. The feelings are conflicted, but there are some feelings.