My 2cents:
Think of the "house" as determining probable cause in a criminal case. The "senate" is the jury and can convict or not. If a cop got probable cause in a criminal case and then the case went to trial- it would be tossed out for "lack of jurisdiction".
The Defendant (Trump) was under the jurisdiction of the "house" when they "investigated" (well..they didn't but anyway) and found probable cause; but then he became a private citizen and was no longer under "Congress" jurisdiction. Specifically, if Roberts is claiming that he does not have the authority to preside over the trial-that reinforces the argument that Congress does not have jurisdiction to hold trial on a "private citizen".