I believe the immunity you cite refers to being held to account (sued) for slander, character assassination or other things a Congressman says while acting in the performance of his job.
Therefore, unless there is precedent that narrows the immunity, it is whatever anyone claims it is until finally tested with SCOTUS.
Remember the case of Idaho Senator Larry Craig (R) who was arrested for a "wide stance" at an airport bathroom while traveling back home from Washington? Some argued that he should have been privileged from arrest because he was traveling to and from Congress. A narrow interpretation of the privilege would suggest that he's only privileged from arrest for actions or statements he took during legislating.
Then there was the case of Representative Patrick Kennedy (D-MA) who crashed his car into a barrier at the Capitol at 2:45am. Kennedy claimed that he was sleep driving due to taking Ambien, and thought he was going to vote. Some suggested that even this was covered by the privilege from arrest clause, but Kennedy said he wanted no special treatment.
So, the bottom line is that I don't know if it's been tested one way or the other, so I'm erring on the side of broad interpretation.
-PJ