Protecting Department of Homeland Security Personnel Act of 2013 - Prohibits any adverse personnel action, including termination, against any employee of the U.S. Immigration and Customs Enforcement, U.S. Customs and Border Protection, or the U.S. Citizenship and Immigration Services of the Department of Homeland Security (DHS) who refuses to carry out a provision of the DHS memorandum issued on June 15, 2012, regarding the exercise of prosecutorial discretion with respect to individuals who came to the United States as children.