These are nice cushions, and the quilted fabric is luxurious and comfortable, even though the cord is worn through in places.
The cord on these cushions has a jute core, such as upholsterers use. It has worn out the cording from the inside, since the cord was covered with a lightweight chintz fabric.
If you cover your welt cord with fabric cut in the direction of the grain of your fabric it will always be "wavy" like this. Use bias strips (preferably cut at true bias, or 45 degrees) and join them with seams that are diagonal instead of straight across the cord. Free instructions for cutting continuous welt cord can be found here