PeeJay Ess - You mean: "You will have to take care of your 90 day report as usual until the time you're here on your THAI passport." ?
If she re-enters on her US Passport, she will need to report again every 90 days but not if she enters Thailand on her Thai Passport. Wouldn't that make more sense? Don't know.
It is very common that tourists overstay for a day. Mostly because people think 1 month equals 31 days.
If it's just a day you overstayed it's mostly down to the custom officer in front of you. They are more lenient at the international airports then the land borders If it's more than that, you pay. Simple.
The red stamp you get just says you paid your overstay fine. Absolute no problems. I got several of them.
No worries, Just go direct to the over payment counter and pay before you go through customs. Although it will be 500 THB per day. There are no endless lectures as Thomas Lindegaard Jensen suggests.
Easy, peasy, straight forwards.
But be aware, as somebody already mentioned, should you get in to a silly police check, you might get problems.
I'd recommend to go for an extension before you legal time runs out. Extension costs 1920 THB (+ 500 thb a day if you're already overstaying)