I thread the bobbin and place it on the pin, start the motor and hold the thread that comes out the top or side while it winds. The thread breaks off after a short bit but that is okay you don't need that short thread for anything but getting the bobbin started. As long as the thread winding on the bobbin does not break you are good to go.
You are not doing anything wrong. Your thread tension will not affect the bobbin winder as far as I know but I may not be knowledgeable about your machine. In general I have never heard of a machine that uses the thread tensioner for the bobbin. Anyone?
I think you need not worry about that little thread, in my humble opinion.
peace
EDIT: I read that the winder stops after this top thread breaks. That is unusual. Can you just restart the winding? If your machine has a small lever that you push towards the bobbin right next to the winder and it engages the winder. It may be popping back to its' original position which stops the winding. Bernina has this lever.
It is a guide that stops the bobbin when it is full. If you have one one your machine just re engage it and the winder will start again when you push the foot peddle. Hope this helps you a little.
peace