I didn't watch the whole video, but right off, a couple things popped up. First, his iron wasn't clean and tinned. The solder he was putting on the iron wasn't melting. The second issue was that his iron wasn'thot enough. When soldering wires, or directly to a battery, an iron that is a too hot is better than one that is a little to cold. On wires you don't want the wire to slowly heat up to the point the solder flows, as two things happen. First, the heat isn't localized and when the solder starts to flow it wicks way up the wire. Also it gives the insulation plenty of time to get hot and melt. Another point is to use a flux separate from the solder. I still have a pound of fine electronic flux solder from my old days at IBMwhen we used to repair circuit boards. I still use a dab of paste fluxto prevent the wire or contact from oxidizing prior to the flux from the solder coating it. As Gene said, clean the wire and contact first as dirty or oxidized wire or contacts don't solder well.
Don