pretty much what badx said. I use them 24/7 on my maintenance tanks, just because I cant always be there to see a potential breakout, prevention is everything. I also like the water polishing effect.
I dont use them on my personal tanks. I will use copper or a different treatment when needed. My school of thought is: I like to use one if netting a fish out is a last resort, hence large maintenance tanks, I cant be there, I dont want to net them out, transport, and treat, so I use one for precaution. My stock tanks and personal tanks at home I dont use one, but have some in case. I really dont have many breakouts at all, even with new comers. I treat fish that can be treated temporarily with copper and then move to an observation tank to see how they do on their own. Existing fish are almost always fine once they are good. If for some reason I were to have a breakout, I would move said fish to a treatment tank and use the uv sterilizer temporarily to catch and free floating organisms.
If you dont have the setup I do... I would run it maybe a week or two before new arrivals to get it going, then maybe 2 weeks or a little more afterwards to make sure. After that, as long as fish are getting along and there are no frequent squabbles or fighting, they should be good to go with proper husbandry and nutrition.
I cant see much benefit to moving them back and forth, the lifecycle for some of these organisms is hours to a day or two, as well as the fact they arent always waterborne, so it is kind of an all or nothing thing, meaning there wont be much residual effect after it is taken off.
PS I have had good luck with a dose of STRESS COAT MARINE when I move fish...I really do think the aloe and slime coat additions really help to heal scratches from nets and rockwork to heal faster and give some protection.