He has connected the "GND" to the negative output. This generally should work with a few caveats. The first is that the input voltage seen by the buck module is actually the input to output voltage so you have to watch for input range. The second is that getting the enable signal and power good signals right can be annoying since they are referenced to the chip ground which is the output. The attached figure is from the LM2576 datasheet, and it should work correctly as drawn.
I do have a couple of questions:
Is there any reason you are sending the 12V regulated output to the inverter? It would make more sense to me to have the two converters in parallel, one taking +18 to +12, the other taking +18 to -12.
Are you sure your power supply current limit is high enough? The problem could be as simple as hitting the current limit on the 18V supply, causing it to enter current limit mode. Switching regulators don't like this: they try to respond by drawing more current, which draws the voltage down further. Even if you have the current limit set high enough for the steady state the turn on transient can trip the current limit and cause it to fail. This is a good reason to implement under voltage lockout on switching regulators. You don't really want them turning on until the input voltage is ready.