Electronic – Rotary switch for bench supply ammeter

Each of the 3 power rails (3.3V, 5V, +12V) are connected to a fuse, then to a binding post, while the negative binding posts go to ground.

This sounds like the problem. Keep in mind, voltages are differences in potential between two points. There's nothing special about ground, it's just an arbitrary point which we pick. It's 0V because the difference of something with itself is 0.

You can call anything you want "ground". That's why this circuit works. If you call the -12V output as "ground", then everything else is 12V higher. That's including what was previously called "ground": now it's 12V, because it's 12V more than what you are now calling ground.

Now consider what you've done:

^{simulate this circuit – Schematic created using CircuitLab}

The "ground" of the power supply connects all of the voltages supplied together (connections labeled B and C). The output voltages are relative to this. Notice how the -12V (V4) makes a negative voltage because it's positive side is attached to "ground".

Then, you attached the negative binding posts of all the supplies together. Largely this is redundant: you are duplicating connections B and C. But you are also adding connection A.

See the problem? You've shorted out V4. A wire has ideally zero resistance. By Ohm's law, the current that will flow is:

$$ \frac{12V}{0\Omega} = $$

In reality, the wires used to make this connection actually have some very small resistance, and you get a whole ton of current. This far exceeded the current the voltage regulator can handle and the smoke got out.

You can get a reed relay, such as this one, with contacts rated at 200 VDC @ 500 mA, and a nominal coil voltage of 5v. The datasheet is here.

The advantage of a relay over a transistor solution is it would provide total isolation. Also the easiest way of integrating into your current system, just wire the relay contacts across your switch contacts.

Since you are switching a fairly low current, you might want to use a relay with two Form A contacts and wire them in parallel. This relay is identical to the one above except it is DPST (and costs about twice as much).