I would never dose an invert tank with an invert killer. Copper can soak into the silicone and you'll never be ablle to keep inverts in this tank, or at least for ages. Most of the dangerous hitchkihers can't just appear unless they've been brought via plants or other equipment. Otherwise non-harmful ones can appear in a tank when conditions are pleasing them.
Those tiny worms could be detritus worms. They normally kind of take an S shape when moving, caused by overfeeding and left over food. Decrease the food, clean up left over food, increase syphoning and water changes and there'll be soon no strange inhabitants.
Whatever is feeding them and making them multiply won't disappear by adding copper or any meds. And it will make it worse, because instead of being processed by them, it will just rot and develop pathogenic bacteria instead.