Is this the 15G tank that you started? How deep is the substrate? Better describe the substrate that you used and the present livestock in your tank.
Please post full tank shot with white light. Also post close up picture of your substrate showing the algae that you see.
I will make one comment from your other thread which I read. Lower light intensity is easier to control the development of your new ecosystem than intense lighting. When you master the craft and your ecosystem is more mature than you push it with more light. For now, I suggest you add biodiversity and janitors. Janitors are your clean up crew, which should include detrivores to consume organics in substrate. Biodiversity includes consumers & competitors of nuisance algae. It depends on your Reefing style. I have been addicted for 55 years and am a “Laissez Faire Reefer”. Get some help with diver collected uncured live rock.
https://gulfliverock.com/premium-deco-live-rock
https://gulfliverock.com/hitchhiker-id
“so I want to start doing it regularly this time. I want to make sure it shouldn’t cause a spike in the water killing corrals or fish by disturbing the substrate that hasn’t really been bothered”
Not sure how you do partial water changes or if you vacuum the surface of your substrate, but you NEED to. It is not necessary nor desirable to stir up muck, simple vacuum the surface with finesse.
Also, some chemistry parameters would be good to know: salinity, alkalinity, ammonia, nitrite and nitrate readings.