He literally asked her out then she went back to the teacher to cuck him. That's NTR.
Actually the other way around, she asked him out, after being told to do so by the teacher.
Yes, it is NTR, quite literally an intentional in-your-face cuckold setup (by the teacher, not by the girl) to have the boy see her cheat in the middle chapter.
But it is redeemed by the ending, for those that care a bit beyond tags.
P.S. There was a better translation on nhentai as part of the full tankoubon (Gunjo Gunzo) that can still be found on some clone (or source
) sites.