It helps to first use fusible tricot underneath the t-shirt fabric to stabilize it. T-shirt fabric is stretchy, so you are stretching it as you sew. Try using a walking foot (feeds top and bottom fabric evenly) and/or sewing with a strip of tissue paper underneath.
You could also iron fusible tricot to each edge of t-shirt fabric before sewing to sashing; this would prevent stretching. Fusible tricot is available online and at fabric shops such as JoAnn's. It's a good idea to pre-shrink fusible tricot by holding a steam iron above it. After that, you could cut it into strips and then fuse it to the edges of the t-shirt blocks.