They are doing DOT Construction OT work. They are "ON" Duty and being paid by DOT to slow people down in these areas, and hand out reminders to people that refuse to slow down. They work on their days off, and are paid by DOT.
Regardless of who pays them, the taxpayers ultimately foot the bill. Sadly, this is a self-imposed "stupid tax". If people would slow down without the trooper's presence, we wouldn't be paying for this. They don't, so that trooper is a living, breathing "here's your sign" for motorists.