I pass the thread around the original spool pin, so it's entering into the little bobbin thread tensioner from the same angle as it would if it were coming from a spool. I don't wind the thread around the pin, just use the pin as a guide. I place the cone older behind the machine, on the right-hand side (behind the main post, basically).
I don't know if that's necessary or makes a difference but I don't seem to have any trouble winding bobbins from my cones. I do have a good sturdy metal cone holder. I do this on my smaller modern machines and also on all my vintage machines. My 6600 has a built-in cone holder so I use that on that machine.
If the bobbin itself is warped or made wrong, that can cause problems. I've had that happen before, mostly with cheaply-made metal bobbins. Plastic bobbins can also be made wrong, or crack.