the only things you're doing wrong are (1) assuming it's your fault and (2) letting this get you into a panic.
the illustrations at the web site are beautiful but they are not accurate.
assuming you cut everything accurately - and i'm sure you did - it should go like this:
do as the instructions say in regard to lining up the outer edges of the squares with the outer edges of the rectangle.
also, do draw the diagonal line at the proper angle to "divide" the square into two triangles.
do NOT - i repeat - DO NOT sew exactly on the line you drew. instead sew just a teeny bit (about 1/16th of an inch) inside the line. Because if you sew right on the line, when you fold the triangle back it will not line up perfectly with the rectangle. By sewing inside, you can fold and press it to match perfectly BEFORE you trim away the excess fabric from behind.
although it doesn't look that way in the illustration at the website, the second triangle is supposed to overlap the first. to check your accuracy, use a ruler to check where everything is in relationship to the 1/4" seam allowance. (see the illustration below. the dotted line marks the seam allowance) i'll bet your triangles weren't as far off as you thought they were.
did you see the picture i posted (page 2 of the BOM topic) showing how to lay it out using half-square triangles? only one set of measurements and one technique. if you'd prefer more help fighting with the block the way you've started, send me a PM.