Uronema seems to impact more fish today than it ever did before. We treat it with metroplex up front (which also handles brooklynella).
Fish most commonly affected are chromis. Then butterflies (particularly copperband, pearlscale, etc.) and anthias as well. Recently, centropyge (dwarf angels) are more affected by it, and I've even seen it in some wrasses.
@Humblefish has looked at some assumed "spinal injuries" in wrasse and found that internal uronema was present on the spine itself upon autopsy, so it's hypothesized that it's a bigger issue than we thought. However...
I personally don't think it poses much of a threat to a tank full of healthy inhabitants. It seems to run rampant through new additions, particularly of those groups of fish. A healthy, established fish in a tank seems to be "immune" to it. In practice, I've never seen uronema suddenly appear on a healthy, established fish in a tank. Even existing chromis seem unaffected, typically.
So what do you do with this information? Well, I don't know. I don't personally worry about uronema for anything other than new additions. I do run all coral, inverts, rock, etc. through a 72 day fallow period, but I certainly don't bleach it (the only way I know to completely remove it). So for that, I probably introduce it frequently.
I treat all new fish as if they have it to be safe. I do this more to keep that new fish and others sharing the quarantine with it safe from uronema. Don't misunderstand, uronema is a NASTY condition. It's very deadly, but again, for whatever reason I've not seen it harm well-established fish, even of typically vulnerable species, say 3-6 months after addition.
If you want to be 100% safe, bleach and proceed -- especially since you're in early stages. However, if you're not prepared to keep it out of the tank long-term and prophylactically treat fish for it before entering your tank properly going forward, I'd say it's a waste of effort. Remember, you'd have to bleach everything wet that entered your tank from now on, as well -- to be 100% safe. Perhaps it's an unlikely event that you could get uronema from inverts, rock, or coral -- but it's certainly possible. if you bleach, obviously, you'll kill whatever you're adding too, most likely. So even in my own tanks, I don't worry about my resident fish being impacted by it.
Admittedly though, I've learned the hard way over the past 18 months how much more virulent it is these days. Whether that's because of the overall weakened condition of the fish we receive these days or because the uronema itself is truly more virulent -- I do not know.
Velvet's recommended fallow period is 60 days. We extend to 72 to cover ich as well.