I don't know if this has been said, but I think the painting was applied long before the drawing.
Look at the leg of the upper nymph (red arrow) and the border of the pool (also red arrow). It could have not been drawn while the parchment was stitched. It was drawn before the parchment strip. Once stitched, the painting was applied, that's why there is no painting at the inner side of the stitching (blue arrow).
I know that we cannot determine the time lapse between the drawing, the strip, the stitching and the painting, but this is the order of the actions for sure.