I don't know the scientific name of it but it is definitely Turf Algae.
Miserable stuff and really difficult to remove. Usually requires manual removal by removing the rocks and scrubbing the bejeebers out of them - I've used a small wire brush on that stuff.
You can either do a water change and use your waste water as a scrubbing bucket, or new saltwater in a scrubbing bucket, remove the rocks one by one, scrub as much off as is humanly possible, give it a good rinse in the bucket of saltwater, and return to the tank. I'd even give the rocks that don't have it (yet) a good rinse to get detritus off them, it will help get rid of the food source for the algae.
What are your parameters, including nitrate and phosphate? Those feed the stuff. In addition to manual removal, you want to cut out the food source because it WILL grow back, and the method I just described may have to be repeated several times over the next few weeks as it regrows. If you don't solve the cause, you'll be repeating it a lot more before you get the upper hand on it.
That bit in the substrate, I'd just grab it out and whatever substrate is attached to it, and remove it. That will be the easiest part of removing it.
Going forward, don't wait til it's all over the place before repeating the scrub-down - get it as soon as you can, when you see it.
Not an easy solution but in my experience, it's the only solution.
Edit: I see you have your nitrate and phosphate to 0 on a test, but they are still there, being bound up by the algae. Until it's all exported and being exported before the algae can take it up, you're caught in the vicious circle.
Jenn