OOOOH
...First, let me say that that I like your cult members' masks; very cute~. And now, to actually answer the question:
I don't have a lot of experience writing about cults, across all my dozens of stories I've written 2 total, and one of those was fanfiction so the foundational work was already done for me. ^^;
But in the one that's actually mine, I've tried to focus on (a) the members' outward justifications for following their leader, (b) the more subtle/implicit pressures that force them to toe the line, and (c) in the case of the MC, how difficult it is to leave it all behind.
A: Family is a big thing with them. Because of the way the cult works, pretty much all the male members are half-brothers or full brothers (some of the older ones might be uncles...I'm not gonna get into it). The leader is the father, of course, and most of the brothers claim that the violent deeds their father orders them to commit are all out of paternal love for them. And conversely, that they 'owe' him their own love and loyalty for the gift of being brought into this world.
Basically, their speech is very positive and intimate in this specific way; there's some stereotypical 'glory' and 'chosen one' talk, but mostly they sound and behave like one big toxic family.
I really love that in a cult; really I think all cults should appear to be a positive or at least a relatively safe place most of the time. It's the reason why people stay in them, after all. You have to make your cult feel like it 'works', like it does its job and gives its members a feeling of security and belonging, not just creepy tasks to perform with no motivation behind them.
B: The above is just what they say, however. ^^; Really, what has more to do with their loyalty is the violent and punitive nature of the cult's activities. They fight...all the time. They hunt, they spar, and they kill each other in ceremonial battles, and the best killers get the highest ranks, along with more privileges and authority. You maintain your rank by following Father's orders (usually, to execute those who are disobedient), and by killing anyone who challenges you.
There's a religious aspect to this behavior, where their specific interpretation focuses on being able to protect the group from outsiders...but it, like, hyper-focuses on this, to the point where the cult's members are raised to feel like their only purpose is to fight and ultimately sacrifice their lives. And unlike in the ancient times when these traditions began, they're no longer being violently persecuted...so ironically, they spend ALL their time slaughtering each other to prove that they can protect each other from enemies that don't exist. ^^; It's just multiple layers of folly, that probably has plenty of real-life parallels...
I don't think every cult needs a thematic backstory like that, but it's fun when they do. 'Cause we all know 'cult=bad', but to spotlight how the very nature of a cult is self-destructive really hammers the point home. When you place all your faith in your leaders and customs and never think about the reasons why, these are the kinds of nonsensical systems you can contribute to...end eventually fall victim to.
C: Leaving a cult is one of the hardest things you can do. Having to change your whole worldview and rebuild your sense of self-worth from scratch...I think it's very appropriate that we call such people 'cult survivors'.
And these problems still apply even when you weren't having a good time in the cult to begin with, as is the case with my aforementioned MC. ^^; When he was younger, he was kind of runty and anxious, and was bullied mercilessly for it by his brothers...things got better for him after they discovered he was a 'chosen one', but he never really recovered from the way he was treated initially, and this eventually led him to be dissatisfied enough to leave.
I won't deny that, as a writer, this feels like 'the easy way out'. ^^; Like, "of course HE could leave the cult, everyone was mean to him, and he even has special powers to protect himself from retribution".
But realistically...that's not really how trauma works? Especially in a cult; when you have trouble fitting in, often your first thought isn't "these people suck and this way of living is wrong, life will be better out there".
You can get there, but usually you start by thinking "...what's wrong with me?" Over and over, in a thousand different ways, for years or maybe decades.
It's HARD to stop blaming yourself when it's all you've been taught. You can't conceive of a you that deserves to exist the way you are when every authority in your life has told you otherwise. And even when you finally meet new authorities who tell you new things, those old lessons are hard to shake.
MC's 'special powers' don't do anything to help with that...if anything, they add to it by reminding him of where he came from and what his 'true purpose' is every time he uses them. And unlike an old habit that you can eventually unlearn, they are a permanent part of him that he can never get rid of or forget about. In a way, I guess it's a kind of metaphor for the lasting trauma that a cult can leave on a person, 'the wounds that never heal', that sort of thing. ^^;