Yes, the "wrong wiring" would actually be correct in this case. The load output of these units is just a set of relay contacts--a switch--as is a normal thermostat. You connect the control lines for the furnace to that switch and it turns the heat on and off.
As I said, I don't have any specific personal experience using any of these devices, but based on what I've seen and understand I think this one would work just fine. Presumably most of them come from the same few factories in China, even if they have a dozen different brand names stamped on.
(If the included wire for the probe isn't long enough, you can extend it with pretty much any old wire that is convenient.)