I dont understand what you are doing for changing axis of each layers of the array.
I am really sorry, but I do not understand what you don't understand about the Array axes.
(You are probably talking about the First Pattern as in your question title...the second doesn't use an Array Modifier).
Hey oolivierduchossoir,
In the array modifier, change the factor to 1, in the axis you want the array to work.
i.e. Constant offset only enabled - X = 0, Y = 0, Z = 1, this will array the model in the Z direction by 1 meter, as in the lesson.
Have a play with the array values to get an idea of what it does.
Hope this helps!