You ended up with it square because the corners you added haven't been trimmed for the next pieces to be added. This is a picture of an octagon piece with multiple borders.
http://files.ctctcdn.com/1c50729e001...900a847439.gif
I haven't watched all this Youtube video, but Karen Lukac does show it with a smaller border, then a larger one.
https://www.youtube.com/watch?v=4W_EnkKyrX4 Perhaps watching this will help you solve your problem.
Edited to add: I see this is the same video hoprigmom refers to. I'm going to have to watch it to see if it is how I would have done it if I had no instructions.
2nd edit: You really need to watch the video. You have to continue using strips instead of using triangles on the corners. FYI...Karen's way is not the way I would have tried it. Mine would not have worked out. HaHa!