I think you're confused about civil versus criminal violations. Just because a violation is civil does not mean it can't have serious consequences.
JP Morgan was sloppy in it's mortgage approvals contributing to the financial crisis of 2007. Do you think that's not a serious matter? That was entirely a civil, not criminal matter.
And overstaying a visa has serious consequences. It's not a fine and you can go on living in the US illegally. You will be deported and receive a 3-10 year ban on re-entry. Reenter again and it's criminal matter.
But you're also ignoring the numerous criminal violations that occur with illegal immigration. Illegal entry, reentry after deportation, immigration fraud, using fraudulent documents, human trafficking, recieving social services reserved for citizens. All of these are criminal violations.
And no, investigating a possible civil or criminal matter and detaining people while you conduct your investigation has nothing to do with due process. Police and immigration officials need these limited powers to do their job. Each of these people detained will either be released or stand in front of a judge, which shows they received due process.