Here is another article, headline:
"Departments of Justice and Homeland Security Release Data on Incarcerated Aliens—94 Percent of All Confirmed Aliens in DOJ Custody Are Unlawfully Present"
https://www.justice.gov/opa/pr/depar...94-percent-all
I believe this also comes from the recent report that the OP does.
I think 94% constitutes more than a majority of them being "unlawfully present".