Many DC devices have capacitors on their power rails. When they are plugged in, they generate a huge current spike as the capacitors charge up (limited only by the resistance and inductance of the capacitors/wires). This is enough to overwhelm the power supply and cause a reset.

The solution is a current limiter of some sort. Sometimes this is as simple as initially powering the USB port through a resistor, watching until the USB voltage gets high enough, then switching over to a direct connection.