Could you be more specific about what made you think that?
***Warning: This is another lengthy comment with potential spoilers. However, you did ask for specifics that back my view on Emma showing sudden changes that contrast with how she initially is portrayed.
What I detailed in my previous comment was along the sexual modesty/faithfulness path. Obviously, taking any other path will involve Emma displaying thoughts and behaviors that are even more discrepant with how her personality was initially described and in even starker contrast to her initially expressing so much discomfort in relation to the married couple's living arrangement with Martin.
As an example, I now will provide the choices and outcomes involved in one of the other paths below, which I suppose can be called the cheating path since Emma conceals from her husband every sexual interaction she has with Martin:
Patrick tells Emma she should be proud that in many years she is the first to attrack Martin's attention
Patrick tells Emma he is okay with her modeling in lingerie if she is into it
Patrick tells Emma he is okay with Martin touching her to adjust her pose or clothing while photographing
Patrick tells Emma he experiencing a whirlwind of emotions when he noticed Martin looking at her in a thong
Patrick stops and watches Emma in the changing room as Martin watches her
Unknown to Emma, Patrick watches her looking at Martin as Martin masturbates and calls out her name while watching porn
Outcome: Prior to her husband's presence in the dressing room, Emma thinks to herself that she is excited and enjoying Martin watch her while she changes clothes. After noticing her husband also watching, Emma says that she is curious about teasing both men at the same time ("something I wouldn't have even dared thinking about before"). Then later while looking at Martin as he masturbates and calls out her name, Emma removes her bra so she can touch her bare breast while stimulating her clitoris with her other hand.
Patrick tells Emma that he is feeling pretty turned on after she shares with him that she was feeling embarrassed and excited about Martin glancing at her and touching her to adjust her pose during the photoshoot
Patrick tells Emma that he can see why Martin enjoys working with her so much
Patrick sends Emma a porn clip involving a couple (just one man and one woman)
Outcome: Emma sends Patrick a porn clip involving two men having sex with one woman. As she does this, she thinks that maybe Patrick would have preferred a threesome video with two women instead of two men, but she sends the porn video with two men anyway. After sending the threesome video with two men, Emma thinks to herself that she is both worried and excited. She then showers and leaves the bathroom door open, which results in Martin seeing her bare breasted.
Patrick writes nothing in response to the video that Emma sent (in other words, does not say that he likes it)
Outcome: Emma tells Patrick that she noticed he did not have anything to say about the threesome porn video she shared. Patrick replies that he is "worried these fantasies might turn into something more." In response, Emma says she gets it. Though Emma admits that she probably should not have sent that video, she then cannot help herself but to think about Martin performing sex acts on her instead of her husband as she has a masturbatory video chat with her husband (unknown to her husband, who believes she is imagining him pleasuring her). After the video chat ends with her husband, Emma is still not sexually satisfied and continues to masturbate in bed as she thinks about what she viewed earlier on porn sites. Lastly, Emma decides on her own to drink wine with Martin to celebrate that evening, despite knowing that alcohol supposedly gives her problems with controlling herself.
While Emma is in bed that evening, Patrick makes a noise to distract Martin when he notices him kissing Emma on her legs and ass in bed (with Emma actually being awake and acting as if she is asleep but says nothing)
Outcome: Emma agrees to wear some particularly provocative lingerie for Martin, which she admits makes her look like "some high-class escort." After the photoshoot, Emma allows Martin to place his hand on her butt for the third time that evening, and she then gives him a handjob and licks the tip of his dick until he cums. When her husband asks why she did not answer the phone, Emma conceals all of this having happened from him.
At the end of the next evening, Patrick decides to call to check up on Emma after the party at the home of Martin's brother (after he sees an email indicating that Emma failed to tell him she and Martin would be posing as a couple and would be in a hot tub completely naked together)
Outcome: Emma allows Martin to finger her and grabs his dick while in the hot tub. Then when Patrick calls her while they are on the way home, she allows Martin to stroke her pussy. Then when arriving back at Martin's home, Emma allows Martin to kiss her legs and ass while she is in bed. (Note: If Patrick decides not to call to check on Emma because it is already past midnight, then she allows Martin to give her cunnilingus.) When Patrick asks Emma about what happened at the party and afterwards the next day, she conceals everything from him.
While in bed together on the first night after returning from out of town, Patrick decides to pretend to be asleep when he realizes that Emma is getting up from bed (and assumes she probably is heading to the kitchen or bathroom)
Outcome: Emma joins Martin the shower, gives him a blowjob, and has sex with him in a standing position. As this is happening, Patrick gets tired of waiting for Emma to return to bed, hears the shower and assumes it must be Emma (thinking it would be nice to join her in the shower), and then knocks on the bathroom door three times. When Emma finally answers the door, she keeps him from entering and says she just needs a couple minutes to finish.
On the day before moving into their new apartment, Patrick decides to wait for Emma and Martin to return from viewing photos together (choosing to trust his wife although he heard her and Martin whispering in the hallway)
Outcome: Martin tells Emma he is crazy about her, and during the next evening (the night prior to moving into a new apartment), Emma is given the option of going to Martin's room. If the choice is made for Emma to go to Martin's room, then she gives him a blowjob and has sex with Martin in multiple positions, ultimately allowing him to cum inside of her. If this happens, then the next day while her husband is busy moving (before she and her husband have even slept one night in their new apartment), she gives Martin a blowjob, allows him to perform cunnilingus on her, and has sex with him in multiple positions. Upon hearing her husband return, Emma then makes up an excuse to have her husband go do something downstairs, resumes having sex with Martin, and then again allows him to cum inside of her. When Emma and her husband finally have sex in bed in their new apartment the next night, she is aroused in part by thinking about the professor (Matthew) having flirted with her and put his hand on her knee when they had dinner that evening.
Along this path, Emma's behavior is even more discrepant from how she was presented at first. Despite Emma not being a very adventurous person apart from her husband, never having had sex with anyone but her husband, and expressing discomfort about the living arrangement with Martin four times, within a matter of days and with little initial encouragement from her husband to be open to posing for photos in lingerie and considering fantasies they might explore, Emma has become sexually obsessed with Martin (and the idea of having sex with other men) to the point that she is allowing it to occupy her mind even when she is supposed to be sexually focused on her husband. She further has had many inappropriate moments with Martin and has engaged in multiple sex acts with him, which she has concealed from her husband all along the way. If her husband is trusting of her at various points and does not make special efforts to check on her, she also has full-blown sex with Martin a number of times, which includes having sex with Martin in multiple positions as her husband is busy with helping them to move into their new apartment.
Interestingly, even if Patrick is untrusting and checks on Emma at every opportunity along this path, she still engages in multiple sex acts with Martin, does not have sex with her husband in bed on the first night in their new apartment, and allows the professor to grope her during dinner. Also, in what must be an error in the game, Emma mentions to herself while in bed with her husband in their new apartment for the first time that she is having trouble not thinking about the passion she shared with Martin while they were moving and expects it to happen again and again (when nothing happened between her and Martin while moving if Patrick is untrusting and checks on Emma at every opportunity).