I don't think that's true, because we know the timeline for Sensei's relationship with Niki. He's 31 now. The accident was eight years ago, because Niki mentions that that's how long it's been since they were together. We know they dated for 5 years. So their relationship began when he was eighteen. This makes absolutely no sense for a beginning of his relationship with Teacher -- everything points to it happening when he was younger, possibly even preteen.We also now know that this relationship began after Sensei started dating Niki
I think Teacher is just teasing him in the way a lot of adults tease two close friends of opposite genders when they're kids: "oh, you spend a lot of time with X, is she your girlfriend?" He and Niki were childhood friends.