You can hook as many batteries of differing voltage as you like to a common ground line (usually the negative these days, but in the olde days you got batteries both sides of the line) and there will be no problems until you start having bits of circuit connecting the different voltages. This should not happen.
Relay based systems do have the great virtue that whatever their contact(s) are controlling, the power supply can be totally independent of the model's radio power supply. The connection is just aux battery terminal to relay contact, then other relay contact to one side of load, other side of load to t'other battery contact.
I've had one or two Turnigy products, and they have all done "what it says on the label" and done it well, but there have been obvious economies when it came to writing the instructions in Engrish. Fortunately, the symbols and conventions of electronic circuits are fairly universal, so diagrams don't suffer from translation as much as the written word.
Semiconductor switches do need to be treated with caution as there are so many possible combinations , each with their own virtues and pitfalls. Like Dave says, make your wiring look like their drawing, it will work. Before you can think outside the box, in cases like this, you need to really know what is inside the box.