Perhaps I'm merely being obtuse but how has Sei used her 'position of authority' into intimidating Aya? It's s not like she told Aya she’d write a really good recommendation if she sleeps with her. Sei teaches at a different school, one that's regarded inferior to Aya's academy, so her profession does not really affect the inner workings (outer yes) of their convoluted arrangement. Her being a working adult in society hasn't really come to play either, save for her having an apartment that can serve as their sex dungeon and perhaps paying for things like karaoke trip/groceries/etc.
The intimidation tactic she implemented, threatening to cut ties with Aya if she didn’t meet up with her, could have been done by another high school girl. Unless I'm forgetting something...
As for the guilt trip thing, I agree that she was most likely trying to incur sympathy with Aya in the beginning (the karaoke room) so that Aya would agree to having a sexual relationship, but yet again that could have been something a teenage girl can do. Sei crying about Yoru in chapter 10 was not a guilt tactic – that was Sei genuinely breaking down because she can no longer drown out her past and her traumatic moments are constantly replayed in her mind.
The correct term is ephebophile.
What I'm wondering is this is the truth about what happened... all we heard is the retelling of some stranger who supposedly heard it from Saika herself. Neither Saika nor Sei have really confirmed nor denied. Maybe I'm just a fan of Sei but this manga has constantly been trying to show us there’s more to a character than meets the eye so I'm still wondering if this Saika situation has been resolved or if we're going to get Sei or Saika's retelling of what actually happened.