In her restraining order application filed on Tuesday, Gibson, 37, alleges that Bassas Jorge Puigdollers has continually shown up at Gibson's hotel and house. The last straw was when Puigdollers came to her home and knocked on her door.
"That was crossing a line, so that was really scary," she tells PEOPLE. "I am a single female, so I reacted like anyone would and called 911. I'm very good at reacting calmly in the moment, but then I fall apart later."
Police detained Puigdollers, but did not charge him with any crime.
Stalking scares aren't new to Gibson. In 1989, Robert Bardo shot actress Rebecca Schaeffer at her Los Angeles home. At the time of his arrest, his wall was adorned with pictures of Schaeffer, fellow pop star Tiffany – and Gibson herself.
"I was very young at the time, but it was scary, because I realized that whether you live or die can come down to security," says Gibson. "This woman answered her door and was killed. From then, I've always had good security. I can't let it slow me down."
Possibly BroadwayRight now, the singer is in talks for Broadway roles, but plans to spend this summer mentoring young artists. She has created a youth camp called Camp Electric Youth to "mentor and coach talented young artists to hone their craft."
She's also joining forces with former teen heartthrob Joey Lawrence as judges for the online talent show, Total Pop Star, where contestants vie for recording contracts by submitting audition videos. And next up? A three-week gig at Harrah's Casino in Atlantic City, where she will sing her pop hits and Broadway standards.
"I've got a lot going on," she tells PEOPLE. "So I just put the whole incident behind me and do what I have to do."