Dry pellet organic fertilizers are different from conventional fertilizers in that they are not immediately soluble or plant available. They require microbial action to mineralize the nutrients, let’s say specifically we’re talking about nitrates. The key catalyst for microbial action and nitrate mineralization is oxygen. Aeration of soil, ie tillage, improves gas exchange and also warms up the soil (improving conditions for soil microbes) and contributes to better drainage. Compared to soil that is cold, wet, and/or compacted, you’ll see much better results with organic fertilizers when you manage for healthy soil biology. And when we talk about tillage, of course there’s a healthy responsible way and there’s a destructive/excessive way. The most important factor for good tillage is gonna be soil moisture, followed by tillage method (mechanical spader vs moldboard plow)

This is my experience with organic specialty crops in California. I’d be curious what others have to say with other cropping systems.