Hollywood is used to famous people wandering around, but when Camila Cabello skips on to the terrace of the fancy Los Angeles hotel where she is staying, heads begin to turn. It is the morning after the American Music Awards, where she won four of the five categories she was nominated in. On Tuesday, she gave a knockout performance of her new single Consequences, with a full orchestra, in a ballgown fit for a Disney princess. But today, she looks like a student in jeans and a checked shirt hanging open over a Pink Floyd T-shirt. She asks that I sit next to her, rather than across from her. “I like to be close,” she says, shuffling up the sofa. She talks fast and at volume, in long sentences that eventually loop back to a point she was making five minutes ago. Considering that she is the pop star of the moment, she seems oddly unselfconscious.

Cabello rose to fame as a member of the American X Factor-created girl group Fifth Harmony. As is often the way with pop groups, there is usually one you can’t take your eyes off. Cabello was that one. Even in the pop game, natural charisma is rare, but it was obvious from the audition stages of the show that she had buckets of it. Within moments, most of the people in the restaurant we are in are trying to pretend they aren’t looking at her.

At 21, Cabello has had the year of her life. She has been draped in accolades for her debut album, Camila, and its addictive, inescapable single Havana. It wasn’t Cabello’s debut solo single – towards the end of her time in Fifth Harmony, she had tried a few tracks and collaborations on for size – but it was the one that felt most like her. It almost wasn’t a single at all; her label wanted her to go with a song called OMG. Cabello fought for Havana. She had a gut feeling about it and suggested they put both out to see. Only the latter made it on to Barack Obama’s 2017 end-of-year playlist, and it has been streamed more than a billion times. “Everybody was like, it doesn’t have enough production, it’s not radio-friendly enough, it feels too slow, it’s a cool piece, but people won’t get it, only Latin people will get this. And I was just like, let’s just put it out and see what happens.” She smiles. “And …”

I imagined some executive grumbling that it was too Latin, and ask if she was insulted. “No! The people who said that were my family,” she laughs.

Cabello was born in Havana to a Cuban mother and Mexican father and lived between the two countries until her mother brought her to Miami when she almost seven. Her father followed 18 months later. “I had a Disney calendar where I would X the spots until my dad met up with us in the United States,” she recalls.

Her family have always referred to her by her middle name, Camila, although she was born Karla, but she was too shy to tell anyone at her new school that she preferred to be Camila. It wasn’t until she auditioned for The X Factor, at 15, that she publicly reclaimed Camila. “They asked if I wanted a stage name, and I said Camila because I hated my name. I hated Karla. It was like this rebirth. I got to create myself again. I was Camila, and then suddenly I didn’t have to be this shy girl in the classroom.”

Her shyness is something she has to deal with, even now. “I noticed yesterday, I get really nervous before awards shows, and whenever I go up to accept an award, like the first thing I think about is: fuck, now I have to …” Her hand jerks up to her mouth. “Sorry, excuse me!” She is hyper-aware of her young fans to the point of trying not to swear. She starts again. “Now I have to talk in front of all of these people because that’s not my comfort zone, you know?”

She has a way of darting around seemingly unconnected subjects and lassoing them together, and at this point returns to moving to the US as a child. “I never thought about it when I was little, but there is something shocking about moving to a new country and not speaking the language.” When her new teacher asked her if she spoke English, she remembers, she lied and said: “Yes.” She puts on a thick accent to mimic her younger self. “I haven’t even said it until this interview, but I feel like there are memories of me being very introverted and shy when I was in Cuba. I hated family parties. I would start crying and lock myself in a room because I was overstimulated,” she says.

Cabello (far right) in Fifth Harmony in 2013. Photograph: Amanda Schwab/StarPix/Rex/Shutterstock

She considers herself an unlikely pop star. “I always hear stories of people who became singers and musicians who put on shows for their families when they were very young or were the class clown or always singing in class, and people saw it coming for them. I don’t think people saw this coming for me.”

There’s an appealing element of tenacity that runs through Cabello’s career, a kind of bloody-mindedness about doing what feels right even when the advice suggests otherwise. I wonder if she feels that such determination is connected to her experience as an immigrant. “That’s like, 80% of it,” she nods. “I feel like it’s the model that I saw in my parents and in my family, how they just didn’t take no for an answer and were always the underdogs – that made me have the same kind of fire that they’ve had all their lives. Constantly starting over, just using will, not even talent, not even skill, not anything, but just sheer force of will to be able to do things.”

Cabello is happy to talk about her family’s experiences of coming to the US because she thinks it matters to hear human stories. At the Grammys in January, she gave a speech in support of the Dreamers, the children of undocumented immigrants fighting to stay in the US. “I’m a proud Cuban-Mexican immigrant … and all I know is, just like dreams, these kids can’t be forgotten and are worth fighting for.” She once left the stage with Fifth Harmony shouting: “Don’t vote for Trump!”

“It definitely hits really, really hard,” she says, of the current hostile climate. “I feel like, with everything in life, there has to be some kind of emotional trigger for people to look at something differently. When there’s just statistics, and talking, I feel like people lose the humanity.”

Cabello performs at a music festival this year. Photograph: Rick Kern/WireImage

She was impressed by her close friend Taylor Swift – whom she recently supported on a global stadium tour – asking her fans to vote. “It’s amazing, there’s 65,000 new [voter registrations].” Cabello says she will “definitely” tell her fans to vote, but hasn’t thought about whether she will reveal how she is voting. “I feel like I need to inform myself more on all of the people before I even vote. I’ve been pretty open about stuff in the past though, so I’m not afraid of being open. I just need to take the time to read up on it.”

When she was little, Cabello wanted to be on the Disney Channel; her parents said she could audition for something, but only once she turned 15. When she did, instead of having the traditional quinceañera celebration, she asked them to drive her to North Carolina, 14 hours away, to try out for The X Factor. The producers told her she was an alternate who might get the chance to audition if there was time at the end of the day. For the first two days, there was no time. When she finally did sing, her cover of Aretha Franklin’s Respect wasn’t even broadcast. “I was so sad,” she says. But they liked her enough in the end to pull her into a group with four other girls, One Direction-style. Fifth Harmony were only third in the contest, but they were the ones who became stars.

Cabello singing Aretha Franklin’s Respect.

They were together for almost five years. Cabello started writing songs when she was 16, but the band had a five-album deal, so she assumed she would give them to other people. “I just wanted to cultivate my songwriting muscle. But then I was like, these stories are too close to me, and I’m kind of a control freak. I just like doing all of it.” Her solo ambitions fell foul of the Fifth Harmony vision and, in December 2016, they released a cutting statement informing their fans that Cabello had told them she was leaving, via her representatives. Cabello hadn’t known it was coming, and the animosity continued: a few months later, the group’s first performance as a four-piece saw them theatrically pushing a fifth figure off the stage at the MTV Video Music Awards. She thinks that being a teenager in that situation made it infinitely worse. “If I were older, I would have felt it differently. I think everybody would have handled it differently. But being really young was really hard and scary because I didn’t have enough life experience to, I don’t know …” She trails off. “Yeah, that was really, really hard.”

Cabello. Photograph: Emma McIntyre/Getty Images for L'Oreal Paris

When Cabello writes notes to her fans online – apologising for not being on social media enough, or announcing a new single, or even giving her side of the Fifth Harmony story – she always signs off with, “love only, Camila”. It is something she used to tell herself in the aftermath of quitting the group. “When I left the group, and when all that stuff was going on, I started to use this mantra to myself, of ‘love only’. Any time that I would feel scared, any time that I felt doubt, any time that I felt like I couldn’t do it, any time that I felt there was conflict between any of us, or on the internet, I would repeat to myself, and say to my fans, love only, love only. When it comes to the internet, it’s a powerful thing to say, because there’s no hatred here, no anger here, no resentment, no bad feelings, I don’t want any drama, I don’t want any negativity, just, love only. I won’t let anything else into my sphere.”

Consequences marks the end of the Camila phase; Cabello is already working on its follow-up, though she can’t tell me anything about it yet, other than that she intends to stay in Miami to work on it in the house she bought for her family last year. “I can’t be away from home any more.” True to form, she had to fight for Consequences; people wanted her to release She Loves Control, an upbeat empowerment-banger that leans towards her sensual Havana side. But she decided to do a new orchestral version of a ballad instead.

She brings up what her producer Frank Dukes said when she was weighing up recording a song that she knew would be big, but that she didn’t feel close to. “He gave me a good piece of advice, about protecting your excitement. That’s so true because, hopefully, I want to have a long career.” After the year she’s had, I laugh at the “hopefully”, and she looks aghast. “Well, it’s not guaranteed! You don’t know. I don’t know.” She sounds every inch the underdog. “But I’ll give it my best shot.”