The less you disturb amended clay the better
Because of the many benefits that accrue to soil quality, it is clearly in your short-term interest to incorporate organic matter regularly and deeply, at least when beginning the process of whipping a clay soil into shape. Soil particle aggregation and aggregate stability, water holding capacity, drainage, nutrient retention, and plant root growth are all increased when organic matter is incorporated.
However, major losses in soil organic matter content can take place when the soil is inverted or mixed annually by tillage. Extensive tillage stimulates microbial activity (gives the little guys an appetite, so to speak), and the consumption of mass quantities of organic matter ensues. After your clay soil becomes more friable and you have provided a deep root zone for your garden plants, you should consider reducing tillage. Switching to a minimum-till system increases soil organic matter, soil organic carbon, total nitrogen, and soil microbial biomass carbon and nitrogen content, especially at the surface and in the top 2 to 4 inches. Because the soil remains undisturbed, fertilizers and other soil amendments do not become homogenized in the tillage layer. Plant feeder roots, therefore, tend to proliferate in the top 2 inches of fertile topsoil.
For a number of years now, I have been experimenting with no-till vegetable planting in the spring. I take a big knife (i.e., a machete), make sure there are bandages available nearby, and scalp the cover crop at the surface, killing it but leaving the biomass in place. I pull the residue apart just enough to dig a small hole with a trowel, drop in my tomato, pepper, or melon transplant, and pull the mulch back around the stem. I plant large seeds the same way, except that I leave a mulch-free window for sunshine to strike the seedling when it emerges. For small-seeded vegetables, I generally stir the soil a bit more and leave a strip of mulch-free surface above the seed.
Fruiting is delayed a bit because the soil is cooler for a time, but overall production is not sacrificed. The mulch reduces weed growth and prevents soil that may carry overwintering disease pathogens from splashing up on foliage. Infiltration of irrigation water and rainfall improves, as does soil moisture retention.
The residue decomposes much more slowly than if I tilled it in. Slower decomposition can result in more favorable timing of the release of nitrogen from the legume cover crop.