The songwriter's father, Ken, is a big-time music producer who's worked with Fleetwood Mac, Billy Idol and his very talented daughter. Caillat, 29, will sing Sunday before the San Antonio Spurs take on the Miami Heat at the AT&T Center in San Antonio, Texas. And just in time for Father's Day, Caillat shares how he has shaped her as an artist.
"My dad is one of the sweetest human beings around," she tells PEOPLE. "He's so patient with people and has so many ideas that he's so much fun to work with."
The father-daughter duo collaborated on Caillat's 2007 breakout album Coco – featuring her endless infectious hit "Bubbly" – and next three projects.
Not that making music together is always easy.
"It's so funny because when you're working with an acquaintance or someone else, you're being more polite,” Caillat jokes. "I find that I'm a little bit more of a brat when I'm in the studio with my dad … so I feel bad."
But Caillat has learned a lot from her father, including how to navigate an industry obsessed with image.
"He always wanted me to enjoy it and be myself. That's something that my parents always tried reminding me when I was younger," she says.
"I was always trying to dye my hair and get these weird haircuts and pluck my eyebrows. I was always trying to find myself. And they were always the ones who were like, 'You're beautiful as you are.' … They know firsthand that it's a really crazy work environment, and the people around you, you don't know who to trust. They always just remind my to enjoy it and be myself, and to stand my ground."
It's a tough lesson – and one that Caillat tackles in "Try," a beautiful ballad of empowerment off Gypsy Heart Side A, the five-song EP she dropped Monday to preview her album coming out later this year.
"I was venting to them about how people in the business around me wanted me to be someone that I'm not. They wanted me to dress a little sexier and kind of change the artist that I was, and I didn't know what to do because I thought, okay, if this is what people are wanting, should I change?" she recalls. "And they were like, absolutely not … you don't have to try to be someone else, because people like who you are."
To spread that message, Caillat created a now viral lyric video, inviting fans and famous friends like Miranda Lambert, Sheryl Crow and Sara Bareilles to send in selfies – all showing their makeup-free, natural beauty.
Caillat also started to live by her lyrics, refusing to touch up the Gypsy Heart album art and promising to perform without makeup for some concerts.
"I have a mole on my forehead that they've always taken off every single picture of me, and they've made my arms smaller if I gained a little weight before that photo shoot," she explains. "I've always allowed it because I thought that's what people liked better. And now I'm completely changing that.”
Being photographed totally fresh-faced may make a lot of women nervous, but for now, Caillat is more concerned about Sunday's performance. Though she's sung at athletic events before, the different crowd and pressure of live TV always give her stage fright, she says.
"It's so terrifying, it's so much pressure, so it's a really scary experience," she tells PEOPLE. "But so much fun. Once I'm done, I'm like, oh, well I just did that, it was so crazy and I got through it.”
See Caillat sing her heart out Sunday during the NBA Playoffs at 8 p.m. ET on ABC, and watch her lyric video for "Try" below.