Phasma's character is discussed in great detail in the 2017 novel Phasma1 and, while it doesn't directly answer this question, it does give us some good clues. In particular, it tells us that:
Phasma's first loyalty is to Phasma, and her second loyalty is to strength
Phasma is going to do whatever it takes to advance herself, and has no qualms about stepping on her allies to do it. This is neatly summarized in a short section of Captain Cardinal's - the only other stormtrooper captain in the First Order - internal monologue2:
As a teen girl, she purposefully disabled her brother with a knife and watched her parents die, then...painted her body with what was left of them to cement her next loyalty. When she accepted that salve, she became Scyre. And he already knows what happened to the Scyre3. Armitage thinks he's got a Kath hound on a leash, but what he's got is a rancor just waiting for the gate to open. No one will see the real Phasma until the moment when what the First Order wants is no longer what she wants. One day - and it's coming - Phasma will betray them all. Just like she did her family, and just like she did the Scyre.
Her loyalty? Means nothing.
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At the very end of the novel is a short chapter from Phasma's own perspective, where she doesn't go quite as far as Cardinal says, but does say outright that she's not willing to die for the First Order:
Phasma was happier with the First Order than she had been with the Scyre, but she would never be willing to drink poison for any master.
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What's more, the novel demonstrates a few times that, when you put her at a disadvantage, she's willing to go along with it until she gets an opportunity to turn the tables on you4:
- As co-leader of the Scyre, she pushes for more warlike, expansionist policies against her brother's preference for diplomacy. She generally yields to him publicly, but takes opportunities to undermine him when she finds them
When Brendol Hux is injured and the group has to rely on a station full of obviously-insane droids to heal him, she goes along with their demands, which basically amount to debt bondage:
"To be blunt, either we take jobs to pay them off, or Brendol dies."
Phasma considered it. "So we need Brendol whole, and we need to know more. We should accept these positions, gather the information we need, and escape."
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"We're happy to be here."
"Very good. I hope you will consider bathing and dressing in your uniforms now. Poor Deefoursevenseven was quite disturbed by your insubordination. You will need to eat before your shift, and punctuality is important."
Siv looked to Phasma, and Phasma just shook her head. "We're happy to comply."
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Later on they're captured by a bread-and-circuses society (who don't have any bread), and are forced to fight for the city's amusement. Phasma goes along with it, taking a mighty beating in the process, until she can devise and execute an escape plan
All of which is to say that Phasma's behaviour when captured by Finn isn't out-of-character for her; she has good reason to believe that she'll be killed if she doesn't comply, and her normal strategy in that situation is to comply until she gains the advantage. It's just that the second part of that never comes around in this case.
1 I know; I'm as shocked as you are
2 Though bear in mind that this monologue is filtered through three levels of bias:
- The original source of the information is Siv, a clanmate of Phasma's from the Scyre; she's an eyewitness to, and later a victim of, Phasma's opportunism
- Vi Moradi, a Resistance spy who heard Siv's story from the source. She's telling the story to Cardinal in exchange for her life, while also trying to get him to defect to the Resistance; in fact, she outright admits (in her internal monologue) to embellishing the story a little bit to get under Cardinal's skin
- Cardinal himself, who has hated Phasma since basically the first moment he saw her
So, although the outline of the facts are certainly true, we need to take some of the emotional colouring with a grain of salt
3 Phasma's betrayal of the Scyre is a significant part of the novel that's hard to find quotes for, but the summarize:
- She directly disobeyed the clan's co-leader, her brother, on numerous occasions, which led to the deaths of several warriors
- She absconded in the night with the clan's four best warriors, their only healer, and their only medical equipment
- When the remaining Scyre people track Phasma down, she leads the battle that kills all of them and personally executes her brother
4 As with Cardinal's monologue from earlier, bear in mind that we're hearing this story second-hand, with Siv's possibly-biased eyewitness account filtered through Vi's somewhat-unreliable narration