Through-hole solder sparking
If your circuit is connected the way it is shown in the schematics, then there really shouldn't be any reason why it is emitting smoke. That is very strange. The first thing you should do is remove the leads supplying the power and check the board for shorts. If you can't find any, the to be safe, check your Arduino board by using it with something else, and make sure it is still working. Also, try moving the level shifter PCB to a different part of the breadboard, just to be safe as there could well be a problem there. Breadboards aren't 100% reliable.

If the Arduino is working, and you have found no shorts on the level shift PCB, and the same thing happens elsewhere on the breadboard, then the only thing I can think of is you have a broken board and you will need to get a replacement. Not entirely sure what would fail to make it smoke like that, but that would be the only thing left. 

To be sure, you could always supply the board with a different 5V source, perhaps a 9V battery with a 7805, or if you have a power supply, then just put that straight on there too and see if it starts smoking.

It'll be a process of elimination between the 3 components you have: Arduino, Breadboard, Level shift PCB. Chances are you have a faulty Level shift PCB. It happens sometimes unfortunately.