Cute project -
I think if you trim the batting close to the stitch line once you've sewn it, it should turn easily. They look like they're done "pillowcase" style - stitch both edges leaving a space for turning, trim, clip the curves and turn right side out. Turn the unstitched edges in and stitch closed.
The strips look like they're sewn and flipped in a quilt as you go method.
Edited to add - a final edge/top stitching too!