Yeah, the title makes me suspicious, but it could be a cheeky fake out to purposely make people anticipate something that is not coming (even though we're explicitly told it's not coming).
NTR is such a weird fetish, are they imagining they're the other guy? But it lingers so much on the victim of it that it has to be some weird form of self-victimisation, and getting off to it; it's emotional masochism.
It's a tired joke, but is it a cost cutting method to use your own tears instead of buying lube? Just use your own spit my dudes! Have some self respect!
Masochism. People's brains work in different ways. It's kind of like a mental illness. I used to know a girl in school who would cut her hands with box cutters because she liked the scars and it was like a protest against her parents or something. People call it self-harm. NTR is also a form of self-harm. The men who are into it are mentally ill and the women who participate in those relationships are just hedonists or degenerate. Manga just dramatizes all of that, but that's all there is to it. Fetishes can get ugly very quickly. We all have our fetishes and a bit of mental illness but the main thing is control of the mind. Those who do NTR in real life and get enjoyment out of it are just those who lost control of their mind.
To explain it more scientifically—The motivation behind cuckoldry (NTR fans) depends based on multiple different factors varying from person to person. It can depend on their cultural, psychological or biological upbringing. It can also depend on their testosterone levels. Maybe it activates a part of their brain (Hypothalamus, cited from certain studies) that doesn't occur in normal humans (focus on the word "normal").
And to answer your question, they don't self-insert into the man who gets ntred or the person ntring him. It's a third-person view. Most NTR fans on hentai websites are often screaming about how the woman in the NTR hentai is too soulless. So assuming their complaint is that, it can be said that they are more attached to the woman character rather than anyone else. So the woman getting NTRed arouses them in return. The better they know the woman, the more they get invested and attached, and the stronger the response to masochism from the feeling that something precious to them is being taken away. So basically developing a slight parasocial relationship with the woman in said hentai manga. This is also why most NTR protagonists aka the guys that are being NTRed, are portrayed as losers/anti-socials/submissive/weak. This helps the average NTR fan to self-insert into the protagonist so they develop an even great parasocial relationship with the girl in the hentai manga.
So to sum it up—masochistic tendencies, low self-esteem, directly linked with mental health, varies from person to person but above statements applies to the majority.