Okay, now we are into things besides CO2, you are not suing it.
Sediment upheavals often brings up lots of fish poo and decayed plant material, which is loaded with NH4. In the water column or near the top 1cm of the sediments, there's not much NH4, but deeper there often is.

So when you do uprooting etc, you should do a large water change.
This will prevent the algae.

This is true for both types of CO2 or non CO2 planted tanks.
If you run a non CO2 plant tank with less plants, or/and high light, you run more algae risk. Algae are very good at removing very low levels of PO4.

Not doing the water change is a good habit for the non CO2 approach, this relates to CO2 stability. So more care is needed, and rarely do you uproot things in such tanks(once evrery 3-6 months at most, doing a water change after is fine there)

Folks that chronically move their plants around in non CO2 tanks, especially newer tanks, will have chronic issues with algae.

I'm not suggesting that you buy a CO2 system.
You can go either way and is both systems higher PO4 will not induce algae.
Generally if it's not CO2 related, and for a non cO2 tank, that means no water changes to rule that out, then it's NH4 in most cases, at least you can trace the bloom to NH4.........

There may be other things that induce algae, such as temp etc, or more specific species.

But overall, these two items explain the lion's share of the algae issues folks have.
Regards,
Tom Barr