I believe it’s the DOJ who had given Pagliano immunity. Now, why on Earth would our friend Loretta do THAT? She did it so Pagliano would have the right to REFUSE TESTIFYING TO CONGRESS.
The immunity came after Pagliano's apperance before Congress. On March 2, 2016 the Justice Department announced that Pagliano would be granted immunity in exchange for his testimony regarding the email scandal. The request for immunity was initiated by the FBI.
Pagliano pleaded the 5th before Congress on September 10, 2015.