I took my strip set (20 strips) and folded it in half, right sides together, and pinned the top. I held my ruler down with a really firm hand when cutting and made sure I was cutting with the folds of the seams (does that make sense?). I didn't have any trouble with shifting.
I'm not sure what your pattern calls for but mine had you cut two strips the same size for every row. I wanted to cut all my strips at one time (not go back and forth cutting and sewing them), so I cut the two strips per row and pinned the row number to them. This worked well for me.