Correct.
Each house may punish members for their behavior.
No authority whatsoever to punish for behavior prior to becoming a member.
NONE.
It doesn't say it cant be for behavior prior to becoming a member
U.S. Constitution - Article 1 Section 5
Each House may determine the Rules of its Proceedings, punish its Members for disorderly Behavior, and, with the Concurrence of two-thirds, expel a Member.