Could you be more specific about what made you think that?
***Warning: This is a 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 detail below is mostly from the sexual modesty/faithfulness path, and thus it is the mildest Emma path that can be chosen.
On Day 1, Emma speaks to her husband Patrick: "
You've always been the adventurer; I'm all about predictability. How did we end up together with such different vibes?"
The first sentence speaks to the personality traits of the husband and wife. Personality traits are enduring characteristics that are stable over long periods of time. This means that for years ("always"), the husband has been the more adventurous one (tending to engage in new and spontaneous experiences), whereas the wife generally likes engaging in planned and expected activities.
The second sentence is a question that is asked to emphasize how different they always have been in this respect. Again, this speaks to a longstanding pattern of behavior, and personality traits such as this tend to remain stable and (if they change) change gradually over time.
Also, Emma later reveals (through her thoughts) that her only sexual experience is with her husband, which means that she was conservative with sex prior to marriage and has not cheated on husband Patrick.
Soon after meeting Martin and being told that the bedroom is a walkthrough room, Emma replies: "
I appreciate the offer and all, but I can't do this." Emma finds the idea of sleeping with her husband in a walkthrough bedroom so uncomfortable that her immediate reaction is to decline the arrangement.
After Martin leaves the room, Emma tells her husband in private: "
Maybe we shouldn't have come here at all..." Emma again expresses misgivings about the sleeping in a walkthrough bedroom adjacent to Martin's bedroom.
After Patrick consoles Emma and says that her university dream is important, she replies:: "
If I'd known we'd end up in a walkthrough room where the landlord could pop in anytime, I never would've agreed to this." For a third time, Emma makes it plain that she feels uncomfortable being in bed with her husband with another man in a nearby room who might see them in bed.
Soon after that, Emma tells Patrick: "I never used to get into these adventures. Only with you do I find myself constantly stepping outside of my comfort zone." Emma reinforces her earlier thoughts on her husband being the adventurous one.
Continuing the initial conversation in the bedroom, Emma states: "
I never thought I'd be in a situation where I have to ask someone to hold the door while I change clothes. I don't know how we're going to sleep, knowing there's a landlord walking around." For the fourth time, Emma expresses feeling uncomfortable about the living arrangement, particularly expressing dislike of the possibility that Martin could see her naked body.
Continuing: "
In such a tense situation, I even feel awkward changing in front of you." Emma expresses that even in her husband's presence the mere thought of possibly being seen naked by Martin makes her feel uncomfortable.
Continuing: "
If Martin walked in while I'm half-dressed like this, I'd die of embarrassment and bolt out of here."
Later that night on the first day, Emma denies Patrick any kind of fooling around in bed because she's too uncomfortable about the possibility of Martin walking in while they're doing that.
On Day 2, Emma again denies Patrick any kind of fooling around in bed. From Emma's perspective, she misses having sexual intimacy with her husband, but she feels uncomfortable in thinking that Martin might hear them having sex; and she also notes that it made her feel uncomfortable when Martin saw her in bed in the morning.
On Day 3, Patrick tells Emma after they engage in sexual activity in the apartment for the first time (due to Martin not being there): "
What's gotten into you tonight, babe? I haven't seen you this excited for a while." In response, Emma essentially says it's nothing unusual and that she just really missed her husband.
However, from Emma's perspective, the following happened to her while her husband was at work: She tripped and fell and in doing so got a full view of Martin's dick.
Emma repeatedly noted that Martin was staring at her throughout the day and expressed being excited by it. After her husband told her that maybe she should try to be more modest and not call as much attention to herself, she expresses being slightly disappointed because she would like to be a little naughty around Martin. From Emma's perspective, she further expresses being surprised by how much she enjoys being in the spotlight and thinks that maybe it's because Martin is the one who is taking the photos.
She then later admits that part of her motivation for wanting to have sex with her husband so badly is how turned on she feels from the photo shoot with Martin earlier that day (which means she lied to her husband about being excited only because she missed him so much). After having sex with her husband, Emma lies in bed awake that night, thinking that she is still so turned on from the photoshoot with Martin that she could have another round of sex.
On Day 4, Patrick wakes up from having a nightmare about witnessing Emma kiss Martin while on top of him, and after noticing that Emma is not in bed with him, he finds her outside of Martin's room trying to sneak a peek as Martin views/listens to porn on his laptop. Then it is revealed that from Emma's perspective earlier in the day, she is starting to enjoy Martin's attention so much that she forgets her husband will soon return home from work.
On Day 5, Patrick again awakens and notices that Emma is not in bed with him. This time he witnesses Emma peering into Martin's room as Martin watches porn on his laptop. After Patrick expresses surprise that Emma did not turn around and head back to their room, he notices that she is completely captivated, with her legs shaking in excitement. If her husband interrupts her, then Emma says she was just curious after getting out of the shower and wanted to see what was going on inside of Martin's room, where as expected he again was watching porn and leaves it at that. If her husband continues to watch out of curiosity about what she will do, then Emma begins to breath more heavily, puts her hand to her forehead, and then turns around with excitement/emotion on her face.
From Emma's perspective, she got out of bed that night because she heard the sounds of Martin watching porn coming from his room again and could not help but take a look at what he was doing (which means she lied to her husband about being out of bed because she took a shower). In the scenario where her husband interrupts her, Emma still stares at Martin as he masturbates to porn. In the scenario where her husband does not interrupt her, Emma further witnesses Martin call out her name twice while he says that he wants her so bad and that she makes him so horny. Emma reveals none of this to her husband prior to him leaving town the next day.
Then while Patrick is out of town (regardless of path), things become increasingly provocative between her and Martin. Of note, Emma immediately agrees to do a beach photoshoot with Martin in a rather skimpy bikini, even if her husband previously said he did not feel comfortable with her modeling in skimpy attire. After their photoshoot on the beach, Emma then immediately agrees to get in the water with Martin after he removes all of his clothing. Then when she gets a leg cramp, she feels Martin pressing his dick against her ass. When she speaks to her husband later, she omits that they had this particular interaction (the third time she conceals information from her husband). Emma also agrees to posing as a couple with Martin in visiting his brother's home, and she further agrees to get in a hot tub with everyone completely naked.
As you can see, even on the sexual modesty/faithfulness path, Emma acts in a number of ways that are quite discrepant from how she initially was presented.