Performance coach Trapper Felides is known for turning kids into stars, but the Oxygen network wants to make him the next big thing. He’s the focus of the network’s reality show “The Next Big Thing: NY,” which debuts Tuesday right after “The Glee Project.” Turns out Felides is from Rehoboth. He grew up in Southeastern Massachusetts and eventually moved to Los Angeles and New York to prep young people for show biz. Felides told us Monday that he’s thrilled to do his work in front of camera. He also revealed that being an Oxygen star has its perks; he hosted a Tonys screening party on Sunday night and woke up in the penthouse at the Trump SoHo. “My boyfriend was like, are you [expletive] kidding me?” Felides said of the palatial space. Oxygen will screen the first episode of the show at Sardi’s in New York on Tuesday night. Felides promises that he’ll come home to watch some episodes here, too.