ATS and CYANO

Welcome from Italy. The order that nuisance algae are removed from your system, when using a scrubber, is usually like this:

The weaker photosynthesizing algae, which are any of the brown dusty types like diatoms or dino's, go first because they don't pull nutrients out of the water very well because they can't anchor strongly, and thus they can't make use of strong water current (much less, turbulent air/water interfaces) which remove the boundary layer barrier of water insulating the algae. Also they only form on surfaces, which stops flow from going through them. So they are weak filters and need lots of nutrients; when nutrients in the water first start to drop, these algae can't survive.

Next comes GHA (green hair algae), which has more of a translucent "antenna" to catch flow and light; it can extract nutrients from the water longer, and anchor in high flow and turbulent air/water interfaces better (which removes the boundary layer barrier of water insulating the algae), and thus survive by extracting nutrients even when nutrients are barely available. This is of coarse, until GHA is eaten by fish! And since a lot of GHA attaches to rock, as long as phosphate is flowing out of the rock, there will be GHA on it.

Next come the tough ones that have stronger strategies to get nutrients:

Bubble algae concentrates very low levels of nutrients that are outside the bubble, into to high levels of nutrients inside the bubble. Even if nutrients measure "zero" outside the bubble, the bubble will have some nutrients stored inside it, and will take an abnormally long time to deplete these internal nutrients. But the bubble will eventually go away, if nutrients are kept low enough in the water.

Bryopsis, which uses "roots" to extract nutrients deep in rock. Even when nutrients in water measure "zero", bryopsis can survive from nutrients in the rock. So only after depleting the nutrients in the water for a long time, do you then deplete enough nutrients in the rocks, to kill bryopsis. But bryopsis too will go eventually, if nutrients are kept low in the water. If there is phosphate coming out of the rock, the situation can be really confusing because both the bryopsis and GHA can appear to be increasing, even though you have been testing "zero" nutrients for weeks!

And lastly, there is cyano, which does not care about any of this; cyano can "feed" on food particles, so your clean up crew should be increased to consume and stir up all the food particles on the substrate; water flow along the substrate can be increased too, to help with this. This will also stir up the food particles for the corals to eat!