Part of the problem is the referenced 4 pole plug isn't what he has 
. He actually has 1/4" mono plugs (and thus 2 wires out, not 4.) For the plugs you actually ordered from the picture of them they look like the one on the left in the photo above but without the middle pin at the back. From the photo above the two front pins are connected together (and thus that is where one of your wires connects).The two outside pins at the back would then also connect together (just like your current push button switches and the other wire connects to one or the other of those.
Peter