According to Giddens, Durham allegedly killed them "probably sometime early Tuesday morning." Asked whether Durham went to school after the alleged killings, Giddens said, "I was told that he did, yes."
Suzanne Lacey, superintendent of Talladega County Schools, called the killings a "tragedy."
"Like any small town, when tragedy strikes, it affects the entire community, including the school community," Lacey said. "Our focus is to support the school family during this difficult time."
Authorities have not released a motive for the murders. Durham was expected to make a first court appearance on Friday.
Colin Jeffery Haynie, 16, faces four counts of aggravated murder in the shooting deaths of his mother and three younger siblings at their home in Grantsville, Utah. He confessed to their deaths, according to prosecutors. Haynie also faces one count of attempted aggravated murder for his father, who was the only survivor.