As mentioned, an urchin may take to eating dead/dying fish, but they don't generally go for live fish.
With regards to the herbivore vs. omnivore vs. carnivore thing with urchins (and keeping in mind that all species of urchins have different diets) - I had a similar conversation a while ago about a specific species of starfish, so here's my two cents on the matter:
We tend to think of herbivores and carnivores in black and white terms - thinking that something is either a pure herbivore, a pure carnivore, or an omnivore. In reality, though, these terms are more of a sliding scale/spectrum than separate categories, and only the extreme ends of the spectrum have "pure" diets.
For example, cows (well known for being herbivores) have been known to sometimes eat insects (or even mice/in extreme cases, chickens) - this would, by strict definitions, make them omnivores, but they're not considered to be such. Similarly, carnivores eat the guts of their prey, and often end up eating undigested plants in the process - but they're still carnivores. Frugivorous (fruit-eating) toucans also have been known to purposefully eat insects during their breeding season for extra protein, so they may be considered omnivores during their breeding season, but they're not considered omnivores during the rest of the year.
So, a better way to think about herbivore, omnivore, and carnivore is like this:
-Does the species need one or more specific feeds to survive, and, if so, which category/categories are these feeds from?
-On average, what percentage of the species' diet comes from which category? Does a substantial portion of the diet consistently come from more than one category?
-Is the ingestion of each food item purposeful, or incidental? (i.e. Does the species purposefully seek out foods from a specific category when they have the chance to do so, or not? Does it happen to eat foods from a specific category while consuming foods from another?)
-How does the species' diet change throughout the year? (Edit: How does the species' diet change throughout its life? [some species have drastically different diets at different life stages; for examples, Crown of Thorns Starfish are herbivores as larvae/juveniles, but carnivores as adults]).
Pretty much all species will branch out a little from their natural diet on occasion (hence why we sometimes get tangs eating corals, though it is rare), so there are frequently exceptions to the above, but these questions should get you the big picture.
To apply this to tuxedo urchins:
-If the species only requires one food (algae) to survive, then it's likely an herbivore.
-If the majority of a species' diet consists of foods from only one category, and only an insignificantly small portion of the species' overall diet consists of a food outside of that category (say, like a dying wrasse), then it's likely an herbivore.
-If the ingestion of foods from outside of its primary food category is incidental rather than purposeful, then it's likely an herbivore (in this case, there's a good chance the ingestion was purposeful - so one point for the omnivore category).
-Tuxedo urchin diets don't really change drastically throughout the year, so no change here.
So, using the criteria above, tuxedo urchins are herbivores, but they're not pure herbivores (and neither are herbivorous fish, which are really more omnivores, but eating significant portions of algae is uncommon among fish, so they're considered herbivores).
An example of a pure herbivore would be an Elysia species Sacoglossan slug, which only feeds on macroalgae. Several nudibranchs are examples of pure carnivores.
So, most creatures are technically omnivores, but may be considered as herbivores or omnivores depending on the criteria above.
