I have wired a buck (As I recall) transformer not an auto-transformer (Though I have small ones for device testing)
The transformer had two windings ONe wired "In phase" with the primary transformer in the device and the other (The buck coil) out of phase .
Hughs is saying that is how they are doing it.. I won't argue. There is a very good reason to do it this way But without opening it up and taking measurements I can't be sure what they did. Thus I will take their word for it for now since they make the thign.
IF you have an internal schematic I can look at then I can tell you for sure.
But I'm not opening the case.