Jordan Chiles and Grace McCallum as well as coaches Cecile Canqueteau-Landi and Sarah Jantzi tell PEOPLE about Simone Biles' leadership and personality on and off the floor

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Simone Biles is back at home after competing in Tokyo for weeks and stopping by New York City for press appearances.

The gymnast, who won silver and bronze at the Summer Games, reunited with mom Nellie and dad Ron in Texas on Thursday. "Houston, I'm home. Thanks for making sure I didn't have to wait one more minute to see my family @united," Biles, who is a spokesperson for the airline, wrote on Instagram.

The decorated athlete also posted photos of her sharing hugs with her parents after her flight as she was welcomed back with an audience who waved American flags.

Nellie, who's never missed one of her daughter's competitions, told PEOPLE in this week's cover story that they shared a "tough" goodbye in Texas, knowing that for the first time she wouldn't be in the crowd waving to her daughter. (Due to COVID-19 restrictions, international spectators were barred from visiting Japan.)

"She always knows where we are sitting, it doesn't matter the arena. If she's in a competition, she'll look and I'll wave and we make a connection," Nellie said before the Games began. "It's going to be different because she thrives on the noise. The more you cheer, the better she feels about herself."

For more on Biles's Olympic journey, subscribe now to PEOPLE or pick up this week's issue, available on newsstands Friday.

https://www.instagram.com/p/CSNtqtUj4sU
Credit: Simone Biles / Instagram

Biles was without her family in Tokyo but her coaches and fellow Team USA gymnasts were by her side when she prioritized her mental and physical health over event finals. While in Japan, she opened up about suddenly experiencing the "twisties," a disorienting condition that causes athletes to lose air awareness and puts their safety at risk when competing.

Biles missed four out of five individual event finals (all-around, vault, uneven bars and floor) after withdrawing from the team all-around midway through. Teammates Sunisa Lee, Jordan Chiles and Grace McCallum rallied around her and went on to earn silver.

Then, in the days following, Biles became something more than an Olympic champion when she spoke out about the importance of mental health. In addition, her support for her fellow gymnasts saw her become the chief cheerleader in the stands.

"Simone came back and was the best cheerleader. They needed that as well, to see that she was okay and she believed in them," Biles' coach, Cecile Canqueteau-Landi, told PEOPLE about the two-time Olympian's support after the four withdrawals. (Landi and husband Laurent, who is also Biles' coach, returned to Houston on Friday.)

"I know how hard it is for her to stand on the sidelines because that's not who she is. So having her cheering us on meant a lot," teammate McCallum recently told PEOPLE.

McCallum's coach, Sarah Jantzi, also applauded Biles in taking up a leadership role from the sidelines.

"If you were to take their best player out, could they have come and did what these girls did? I don't know, not as well as they did it. Every single kid, they all got together, they rallied and they're like, 'We have this. We got this,' and Simone came over, and was very instrumental," Jantzi recalled of the team final. "For her to come back and say, 'You guys, I believe in you. You've trained your whole life for this. You've trained for this situation to go out there and do your job." That was very huge, it was very instrumental."

Jantzi added, "To see them come together as a team and to be like, 'We can do this.' It speaks volumes on every single one of their character to get up in a situation that isn't ideal never in a million years."

Simone Biles
Credit: Simone Biles/Instagram

Off the competition floor, Biles is the "spunkiest person ever," according to close friend and teammate Chiles.

"She's funny. She's hilarious. Her vibe and energy are amazing. She just has the most outgoing, bubbly personality," Chiles told PEOPLE. "I know a lot of things that people don't see because I'm with her every day."

On representing Texas with Biles and the Landis, Chiles, who moved from Washington to Houston to train with the trio, said, "Pretty sure a lot of people are in awe how there's four of us from Texas here? That's crazy!"

All in all, the U.S. women's gymnastics team was thrilled to have their veteran captain leading them in Japan.

"Having her on this ride definitely is fun, it's a fun experience. This medal is also for her," Chiles said, looking at the silver medal she won with her teammates. "It definitely was a huge thing to have her here."

To learn more about Team USA, visit TeamUSA.org. Watch the Tokyo Olympics now on NBC.