I don't think they were cut as QST's (one square cut along both diagonals).
If you were to cut a striped fabric square into quarter square triangles (QST's), you would NOT get all 4 triangles with the stripes in the same directions.
You'd get 2 vertical and 2 horizontal striped triangles.
x7lillies's guess is probably right (either method) - but the problem (ok, maybe not problem but issue) is the way you've attached them to the center square.
Both ways she suggested end up with bias on the outside.
I would suggest making sure that you really starch that strip or square BEFORE you cut it to help stabilize, and try to handle, stretch and mangle the sewn square as little as possible.
While I hate working with exposed bias (even though I know how to control it), sometimes you gotta to what you gotta do in the interest of aesthetic design.
Are those striped and plaid designs from quilt fabric, or shirting fabric?
It's a great look.