Springsteen, the daughter of Bruce Scialfa and Patti Scialfa is an Olympic medalist.
After winning the medal with McLain Ward and Laura Kraut, the equestrian claimed she called her family.
"I Facetimed them very quickly. She said that they were all screaming and didn't understand anything.
"Just saw their USA team gear. There was lots of shouting. Although I couldn't get much out of it, I know they are so excited."
Sweden won gold in the jumpoff. Springsteen described the experience as "wild".
Springsteen is ranked 14th in the world.
Springsteen, 29, told CNN that the chemistry between horse and rider can differ from ride to ride.
"Some horses are easy to get on with and click immediately, while others can take some time and may be difficult.
"But you need to be patient, and it must be a mutual giving and taking between the horse and the rider."
She said, "I believe the key to getting out the best of your horse's schedule is making a plan in advance. You can choose shows you believe they will peak at.