Been trying to jump in here, but things keep happening around me that I have to deal with.
First of all, its obviously not a transformer. For one reason, transformers don't work with DC, and for another, you need a DC output to power your equipment, which you won't get out of a transformer.
Its an active power supply which converts 12-24volts DC to 5 volts DC.
Which means there is a lot of stuff in there. Including, I'm sure, several capacitors. Which could easily be the cause of the voltage you are getting with it unhooked.
Try grounding the red wire for a few minutes and see if the voltage mostly goes away.
By that, I mean the red wire coming out of the power supply, not the feed from the battery................
Also, various random voltages are always going to be present on various unhooked wires if the meter has high enough resistance and is sensitive enough.
Don't forget just the Seebeck effect, the opposite of the Peltier effect, also known as a thermocouple, will generate a voltage when two dissimilar metals are brought together.
There is very little current produced, but since most meters today have many megaohms per volt resistance, they don't load down a circuit.
After you ground a "leaky" wire, if you still have a few millivolts, try setting your meter on the high amps range and see how much current the device is producing.
Make sure, of course that you do not use the amps range on a circuit hooked to a strong battery.
Always start on the highest amp range and work down. If you get into the milliamp range and still have no reading, then its just stray noise voltage from thermocouples, and random RF in the atmosphere.