The red ones don't seem as invasive as some of the greens and a lot eat it. Anytime I had the reds over the years I didn't put much effort into totally getting rid of it, just keeping it under control. If it does get worse or is starting to be a problem I would deal with it. Diadema urchins will eat it as well and are less bull dozer then the tuxedo. I have also manually dealt with it. I take a course plastic or metal scrub brush and every few days just scrub the crap out of it. The fish with eat the damaged parts and the constant damage doesn't allow the algae to grow. This damages it more then the fish can so you get faster results. As the algae has to use its energy reserves for constant repair, growth slows then halts.
I find a multi prong approach like this is the best way to deal with issues. Keep nutrients under control, fish\ livestock\ food web and manual removal are how you get pretty much any algae issue under control. You probably have sediment buildup in the tank so I would do a good cleaning. Take a power head or turkey baster and blow into all the crevasses in the rocks and stir up the substrate. Pockets of organics are little hot spots of fertilizer that the plants can use for fast growth. I would change or add some carbon as well and tune\clean your skimmer if you have one. This will clarify the water and allow your corals to out compete the algae for nutrients. I would add some mechanical filter media like a soc or floss for removal and a weekly water change till the detritus \ organics drop.
The plus side of stirring the sediment up is the food web will get to feed as well as the corals so let them deal with it. You will have a increase of food web from the particulate matter in the water column and the increase in population allows you to have more cleanup crew. That is how I deal with all my issues. Support the food web and they support the tank. Coupled with chemical, mechanical filtration and water changes fix most if not all algae issues. I have not seen an algae that can withstand this barrage. It just takes a little time is all. Algae took time to get to where it was so it take times to get it under control.