JJ and Eve were destined to end up in some kind of physical situation, from the first moment he met her and she was half-undressed (who answers the door like that in real life?!) They have shown Eve to be so flirty, to the point of desperation, with any man that has crossed her path from Daniel to Eric and to a certain extent JJ. She's lonely, someone who has been portrayed and referred to by Paige as not going long without a man in her life. Now, she's had her dream of singing again dashed, so I see why Eve would reach for physical comfort at that point. JJ just happened to be the one at her door in that moment. If Eric has been by at that point in time with the photos, she would have sought out his comfort and he would have probably ran faster than he did originally.
As to the earlier point about rape and consent, I don't think Eve ever cared two cents about JJ's emotional state. Her intention was always to have Paige see JJ in the manner Eve wanted her to, not for JJ to feel unworthy of Paige. It was always about Paige dumping JJ, not JJ bowing out in a fit of low-self-esteem. JJ's feelings weren't even an afterthought. It's like saying that Daniel raped (or almost raped) Kristen because he was adversarial with her and told her multiple times Brady was too good for her and her plans would never work.
JJ, to me, doesn't make sense. Sure, he felt some sort of physical connection with her with her wrist massage, but I don't buy that's enough to create an attraction to the point of him sleeping with her. If it had been little things building up over time, I might buy it. We know he had at least two drinks at the party (one and Rory urged him to have another), one at Daniel's and whatever he drank at Eve's, so if he wasn't drunk, he was tipsy enough to impair his judgment. Plus, he feels like he has lost Paige. So I see him being down and out, but to go from that to sleeping with Paige's mother. It just feels like the JJ of old who bounced from one destructive action to another.
In a way it fits, but in a way it doesn't. He's regressed to the point when he first came to Salem, but instead of lashing out at others and vandalizing property, he's just doing things to self-destruct. All starting with his lack of explaining his reservations about being physical with Paige. It's not that Paige needed the entire family history, but when it affects how JJ is interacting with her, she did deserve at least some kind of explanation that he's insecure or worried about inheriting his father's flaws and poor decisions. Keeping quiet did harm to their relationship just as her constant doubting and her saying we're on-again-off-again. Succumbing to the peer pressure of Rory and drinking felt in-character, but out-of-character as well. I'm just torn. I see what the writers were doing, but for me it doesn't jive 100% because I feel like JJ has grown enough that he could have withstood a bit more before breaking down.