I understood perfectly, but I'm afraid you are mistaken. As long as the string is being wound the same direction around the spool, the twist accumulates in the same direction. It makes no difference how you handle the spool; from the spool's perspective nothing has changed. I know it's counterintuitive, but that's the way it is.I tried to be clear in my wording. I’ve gone back and reread it. I can’t really improve on it. I even followed up to clarify that what matters is which side of the spool the line is added to and alternating that back and forth as you wind will keep all the twisting from accumulating in one direction but obviously my choice of words didn’t offer a clear enough picture. Language can be funny that way.
Let's say you are winding the string with it coming over the top of the spool toward you. Then you turn the spool over. Now the string is coming toward you under the bottom, but you have also flipped the axis of the spool so it points the other way. You have reversed it twice, so you are back where you started.