Only immune (from detention) if traveling to attend a session of congress. He was headed home.
Not true, it's to and from a session.
They shall in all Cases, except Treason, Felony and Breach of the Peace, be privileged from Arrest during their Attendance at the Session of their respective Houses, and in going to and returning from the same; and for any Speech or Debate in either House, they shall not be questioned in any other Place.