I had to look that pattern up online and it seems to be just a basic triangle. So no, it would not matter which side you lay down to cut your fabric. It is symmetrical.
You may get in trouble because two of the triangular sides are now on the bias and are relatively easy to stretch/distort.
I read somewhere that starching the fabric helps maintain the shape of template pieces - particularly the bias cuts.
It would help to have a picture to see where you are not matching up.
Maybe this helps:
http://emilierichards.com/uploads/BigDipperQuilt.pdf