When I spread aged composted horse manure I cover a strip about 18" deep across the area I'm working so that I'm not working in the manure and then dig that in with a spade. Then make a new strip. When I'm finished with that area I start over. If on the first pass I had the spade edges facing east/west then I work north south. On this pass I dig in another inch. Changing directions helps break up the clods. I dig the sod so that it gets flipped over down deep.
The manure I'm getting is always from the same pile. Nothing is being added and I'm the only one working it and I've been working it for a couple of years. So I know it's aged and it's well composted. I get a few weeds from it. Mostly tall grains that grow so fast that I can pull them, easily, without kneeling. And I get a few parsnips, but don't know if that was in my lawn that I've been conveting to a veggie garden.
The only other things I add are lime if the soil is acid, mine is, and wood ash. I grow very nice tasty heirloom tomatoes, corn, beans peas, onions, garlic, lettuce, carrots, potatoes and other veggies. I have a rule that I only grow leafy crops and root crops in soil if I added the manure the previous season. I count last fall as being last season. I don't add any fertilizer all season. Nothing!
I believe they use beans as the veggie to grow as a test crop. And I believe if the beans germinate the manure passes the test. I'm being cautious here because I don't test it myself.