Anyone who is controlling and willing to invade their partner's privacy has issues, imo.
Short for netorare, its a japanese term.
Thats the most ill go into it. Rather not mention more of it here. If you want to know more google it. Also, as a precaution bear in mind the term is nsfw.
The English word for this is "cuckold," which is a man whose partner committed adultery. (The term for a female victim is "cuckquean.") Cuckoldry was actually a very popular theme in English literature and plays, many of which were comedies. In fact, often the protagonist of the story would be the person doing
the cuckolding. The reader/audience often wouldn't be made to feel pity for the cuckold, especially since they would often "have it coming" in the story.
This isn't a popular theme anymore, though it is interesting to know that it lives on through this netorare. (I'm not really sure how the concept itself is any more NSFW than the rest of the conversation, though.)
It's also worth considering that this is also a fetish, and that there are people who are aroused by the idea of their significant other cheating on them. That said, in my opinion it doesn't sound like actual cheating
if it's consensual and both partners agree on doing it. The cuckold can still feel humiliated (which is part of the excitement for many), but if they agreed to have their significant other have sex with another person, the significant other isn't, by definition, cheating.
That's how I see it, anyway. Food for thought.