I don't think any of the STC-1000's are actually DC models. My recollection is that they all have bridge rectifiers, and some have internal transformers while others don't.
If I'm right (and I'm pretty sure I'm right) it will actually work on anything around 24V, AC or DC, and the polarity won't matter since the rectifier will sort it out.
Even if I'm wrong, only the cheapest DC device would omit the polarity protection diode. Admittedly, a Chinese STC-1000 might fit in that category. So if it is truly DC and not designed by an idiot, it will work one way but not the other, without harming anything.
(I'm an electrical engineer, but I don't have an STC-1000-24V in front of me to check my suspicions. If you don't mind opening it up, post photos and I can tell you for sure)