I partially agree with Daron's answer, the only reason to evolve ultraviolet sensitivity is if it's being used to either avoid predation or find food.
However Daron's explanation of figuring out if an animal isn't poisonous by using UV light doesn't work because poisonous animals want to broadcast that fact in a manner most marine animals can see, ie traditional visible light spectrum. In fact most animal coloration is intentional and driven by the eyesight of other animals, so it's unlikely for an animal or plant to evolve an intentional UV coloration since there is no point to wasting resources creating coloration most can't see.
So instead of intentional broadcasting I'd go the exact opposite, failure to hide. I imagine the adaptation for seeing UV light would be due to a species that relies on camouflage, either a prey species hiding from your merfolk or a predator actively hunting them. This species is hard to see with visible light spectrum due to their evolving coloration that blends into their surroundings. However since most species can't see ultraviolet light your camouflage species hasn't evolved proper camouflage in that range. In other words they 'blend in' in visible light, but stand out when looked at under UV light.
This would imply a few other thing about the species. First they likely live in shallow waters, since if you go too deep in water UV light is blocked by the water above. Second they would likely be bottom dwellers, living on the seabed near the coast, since they need something to blend into to hide. This species would also need to be a staple of merfolk life, either something that they regularly eat or that regularly hunted them in the past, for them to evolve UV sensitivity just to find this one species. On the other side of the spectrum the species is not entirely dependent on humans and either is hunted by, or hunts, many other species otherwise the species would have evolved UV camouflage to combat the merfolk's ability to see them.
If you really don't want to make up a species like this you could always imply the species has gone mostly extinct precisely because their primary prey, or predator, humans evolved an adaptation that made it possible to see them and that the merfolk's UV sensitivity is now mostly vestigial and simply hasn't adapted away yet I suppose.
Going a step further in theory the merfolk may have adapted UV sensitivity due to a species that is long extinct, but after evolving it found other uses for it. I said most species don't have UV coloration because most other species can't see it, but if merfolk had already evolved the ability to detect UV light then it now makes sense for merfolk to likewise evolve coloration in the UV spectrum. The primary reason UV sensitivity is important now may be because other merfolk have UV coloration that they use either for communication or, more likely, as a sexual display somewhat similar to a peacocks tail. Modern merfolk may see UV precisely so they can fully 'see' the intricacies of their fellow merfolk even if the original driving motivation for the UV sensitivity is long extinct. Imagine the merfolk ladies admiring how ultra violet the chest of a mer-man is the way you may hear homo sapiens admiring a man's abs.
As mentioned in comments humans explicitly don't see UV to protect our eyes. However, when underwater the water above a merfolk would already help to filter some of the more intense light so it's possible merfolk could see UV light underwater safely. I imagine they likely would have something like a see through eyelid that closes shut when they come above water to provide protection against the stronger light above water. This would of course imply they can't see UV light above water unless they intentionally 'open' their eye to see it, and in so doing they would risk pain or being blinded by bright lights.
As an aside be careful not to make your merfolk superiors to humans, evolution is about trade offs, they can't be better then homo sapiens at everything. For example better hearing doesn't seem like a necessary evolution for a marine species since sound already propagates much better underwater then above. Merfolk likely would be able to hear 'well enough' for their evolutionary needs underwater even if they had worse hearing then humans above water. Of course you can handwave this away by saying they use sound over long distance underwater to communicate, much as whales do, with an implication that their improved hearing would likely be slanted towards a very specific type of hearing like infrasonic. But my point is less hearing specifically and more a general caution to avoid the standard fiction mistake of creating species that have only advantages over humans. Make sure your merfolk have disadvantages and things they would struggle with out of water or you have to explain how they didn't outcompete regular humans if they are superior to us in every way and able to survive in more niches.
