If you cut the squares at 1 7/8, then there is no allowance for trimming. After sewing the diagonal, cutting and pressing, you can check the patch for square, but cutting at this measurement assumes a perfect 1/4" seam, resulting in a 1 1/2" square before sewing, and a finished 1".
If your triangles are not coming out, you need to verify you are really sewing a 1/4" seam. Here is a good tutorial:
http://www.quiltingboard.com/tutoria...ce-t89997.html