Agree thread might be old, also once the bobbin has a wind on it holding that first thread in place I usually stop the winder and clip the thread as it's no longer needed.
Wondering though why you are talking about adjusting the tension while winding the bobbin. You don't want to run the thread the thread through the tension discs while winding bobbins (at least not on any machine I've used, but I don't know which Singer model you have).