Touching just the solder is OK, though it is better if you can get the wire as close to the metal as you can (not always easy doing it by yourself).
It looks like you struggled to get the pot warm enough for the solder to flow smoothly, which is normally a sign of an underpowered soldering iron. Small low-wattage irons (15W-20W) are fine for soldering small components in place on a PCB, but the back of a pot takes a lot more heating up. Too low a power iron is actually worse here than too high a power. A higher power iron (50W and ideally temperature controlled) will heat up the area to be soldered quickly, before the heat has time to spread all over the back of the pot. With a low power iron, the heat spreads out all over the pot before it gets warm enough for the solder to melt, so there's far more danger of damaging the carbon track inside.
I'd take some cutters and snip off the loose ends of wires as some may move over time or with vibration and possibly ground out the signal.