I'm going to take a wild guess and figure that almost everyone or maybe every single one who is getting picked up has already been issued deportation orders. That's because actually getting someone out of the country isn't usually a one stop shopping process. It never has been.
In the past, if you got picked up and you had a criminal record, you wound up in jail, then court, then jail again until either you serve your time or your deportation orders are processed, then you're deported.
If you got picked up and did not have a criminal record you wound up in court first, then your orders get processed, and at some point soon after, specifically anytime after the orders are issued, you get picked up and sent back to your country.
But they might not come for you for a little while, depending on whether they consider you a flight risk.
The courts did not automatically consider every single illegal alien a flight risk.
Today, in this administration, maybe all of that has changed, maybe even drastically.
Maybe once you've been issued the orders, you're detained at one of those "great money making private detention centers".
This I do not know, but it wouldn't surprise me.