http://www.heritage.org/constitution/articles/1/essays/26/privilege-from-arrest
I said “while in session”. The Constitution article cited in the link basically means they are not subject to civil arrest while they are “in session” or going to/from but it does not keep them from being subject to civil processes. The exceptions cited are treason, felony and breach of peace.
The Constitution states “during attendance at session” not “while in session” as you claim
You should read what you cite: “The clause, therefore, does not provide Congress with any immunity from criminal prosecution.”