In stating they ran parallel they meant that they're investigating the same offences at the same time. It ran parallel, but did not collaborate with, the Mueller investigation. It found more evidence and drew stronger conclusions.
https://www.rubio.senate.gov/public/index.cfm/press-releases...
“We can say, without any hesitation, that the Committee found absolutely no evidence that then-candidate Donald Trump or his campaign colluded with the Russian government to meddle in the 2016 election."
He's speaking directly about the report, and it was linked in the press release above, if you cared to click on it.