(Indirect reply inbound)
When I first started the game I thought Yumi was originally an outlier of the affection system (i.e., does not like Sensei at all); this was noticed by the gods or whatever that is awful in this world, who tried to include her by inducing Sensei's blackouts and making Yumi a major victim of them. Not only did this served as a wakeup call to the newly spawned Sensei, but originally I also thought this somehow is a strange and fucked up way that starts Yumi's path of affection (in a sense of a more "traditional" porn game, or in a sense of Sekai's grooming strategy perhaps).
Because at the time I thought there is no way Yumi would tolerate this without some kind of comeback, like what she did to Nodoka, if she did not like the creepy fuck at all; so maybe through the unconsent kiss she now is assigned with an affection parameter, and is forced to love him now (but I think this might already been disproven later by the fact that she has really been a tsuendere from the beginning)
To add more confusion to the mix, the Concerned has intervened twice when Sensei was "having difficulties", and also claims to know her by a different name (or I think it's the Concerned judging from the all lower case sentences).
So back to prompt, I don't think OG Sensei was just trying to cheat on Maya via Yumi because her unexplained tendency of being intermingled with the fuckery makes me believe that she has to have other roles more significant than just some flings. But I agree that perhaps OG Sensei did have some plans for her (either Akira or something else has plans for her) if those detentions were, retold by Chika, just making Yumi stand there and staring at her; what could that have accomplished?
I don't think Yumi was ever an exception to the affection points stuff, since she requires some to get through some main events, before we get to the forced kiss event.
Nevertheless, I do think there's more going on with her than just the Original Sensei's feelings.
Like you said, the concerned/User3/Pareidolia has gotten involved with Yumi and Sensei before, but, more than that, there seems to be a couple references to Sekai when it comes to Yumi:
There's also how her cousin happens to be the one that Sekai is seemingly possessing.
Then there's how Sensei's wandering blackouts that Yumi happens to be around for, actually seemed odd to Maya:
Yumi even seemed to be the one to stop Sensei from going "into the light" in the 'Not even me' main event, meaning she might be the reason this version of Sensei lasted so long.
Overall: Yumi is an enigma for now.
As for the detentions, I decided to go back and check, and I think there was more going on than just staring:
Chika just seemed to sugarcoat what Yumi said with "stare at her or whatever".
In fact, Yumi actually seemed to expect Sensei to tell her to do things and fuck with her back in the 'Delinquent' main event:
I think there was more than just staring at her, going on, but, nothing actually physical. Unless she's had her memory altered of what actually happened or something, then who knows.
The original Sensei also may have been stalking her:
