Thirteen/WNET is returning as producer of “The First Ten Awards: Tonys 2002,” on June 2.The one-hour PBS telecast precedes CBS’ broadcast of the 56th annual Antoinette Perry “Tony” Awards for the sixth straight year. Once again, Jac Venza and Jeff Folmsbee are exec producers; Mark Mannucci returns as producer of the PBS show. “The First Ten Awards” include the presentation of honors for play direction, musical direction, book of a musical, score, choreography, costume design, lighting designer, set design and honors. CBS continues the broadcast with the presentation of awards for the actors, productions and playwrights. Gary Smith is exec producer; Ricky Kirshner is producer.