Looking only at the picture:
- One of the Picobuck modules has its power wrong. Red to '-' and black to '+'.
- Powering the Nano board via the 5V pin is dangerous. However, I think it should work.
- There is a double ground path to the Picobuck modules. Directly from the 12V 5A barrel jack and via the step-down regulator, through the Nano board and then to the Picobuck modules. The power for the leds can choose to use the GND wire to the barrel jack or can choose the GND through the Nano board.
The real circuit could have a bad connected wire, for example if you use a breadboard. Wrong currents might occur when you power it up or power it down. You could omit the GND wire from the Nano board to the Picobuck modules. You could add protection resistors in the signal wires from the Nano to the Picobuck modules. I prefer that you limit the 5V power to the 5V pin of Nano module somehow, for example maximum 200mA.