Then I solder not the tinsel wire but only the wrapping wire beyond the end
of the tinsel wire? This looks like there is no actual soldering of the
tinsel at all (which is intentional, I presume, to avoid stress points).

No, I think the wrapping wire creates a strain relief for a way back from the
point where you solder both the wrapping wire, the tinsel wires, and the
mating wire.

I think...