Lowering phosphates won't cause algae if you keep your chlorine in check.

The algae fear is a misunderstanding. Phosphates are food for algae, but they don’t cause it—low chlorine does. Lowering phosphates just removes their food source. If your chlorine is adequate, algae won’t bloom.

Use a phosphate remover (lanthanum-based is common). Follow the label dosing—don’t dump a whole bottle in at once. The product will cloud the water for a day or two as it binds to phosphates and gets caught in the filter. That cloudiness is temporary and harmless, not algae.

The two things that will cause algae: letting chlorine dip below 1 ppm, or adding phosphate remover right after shocking. Give it 24 hours between any chemical additions.

You’re fine. Lower the phosphates, brush the walls, run the pump, and keep your chlorine steady.