There are several "mechanisms" involved in the use of cover crops to manage nematode populations and/or to reduce their potential damage. Some are more clearly defined than others, and most cover-cropping approaches actually may encompass more than one of the mechanisms.
Remember that most plant species are hosts to several nematode species, so a cover crop designed to reduce one species may be increasing another; so that is always a constraint that needs to be monitored. Also, what works in the greenhouse doesn't always work in the field!
This approach will be most effective with endoparasitic nematodes such as root-knot and cyst which have a single infective stage. The idea is to plant a cover crop that is a host to the target nematodes in the fall, while soil temperatures are still adequate for nematode activity. Second stage juveniles in the soil, or hatching from eggs, enter the plant roots and establish a feeding site. They progress through their developmental stages towards becoming egg-producing adult females. The trick is to terminate the crop before the nematodes get to the egg-producing stage. By that time they are unable to move or leave the root, so they will die and are not available to affect next year's crop. So, it involves monitoring degree-days for nematode development. It may be necessary to terminate the crop in the fall or to leave it until the spring depending on the rate of nematode development.
Therein lies the danger. What if you don't terminate in time? What if the soil gets too wet to get in there and plow out the roots? The result will be new nematode eggs in the soil.
The idea is that endoparasitic nematodes are attracted to host roots, enter them, establish feeding sites, but are unable to complete the life cycle due to plant responses, toxic products from the plant, etc. A purported example of this is the use of certain radishes as trap crops for sugarbeet cyst nematode. It apparently has worked in Europe but has been less effective when tried here.
Actually, in most cases, we don't really know the mechanisms. However, the nematode population seems to decline at a greater rate under some cover crops than others. Sorghum-Sudan is an example for some nematode species, but it is a host for others. Usually the "action" takes place in the fall before the soil cools down (I think).
The classic example is marigolds which, when incorporated into soil, have breakdown products that kill some nematodes. However, marigolds while growing are good hosts to other nematodes. The toxic products seem to be concentrated aboveground, so the whole plant needs to be incorporated. Water extracts of marigold plants have had some effect when applied through drippers in vineyards (McKenry's work). But marigolds probably don't make a very good winter cover crop!
Various Brassica species (certain radishes, rapeseed, mustards) produce glucosinolates that are hydrolyzed, in the presence of the enzyme myrosinase, to isothiocyanates which are nematicidal. But we don't know enough of the underlying biology and biochemistry yet to use the mechanism predictably. Where are the glucosinolates concentrated, and when? - roots, leaves, seeds? Under what conditions of temperature and moisture do they break down? How much biomass do you need?
Organisms in the soil depend on carbon supplied by plants. Loosely speaking, the more plants that are grown or the more plant material incorporated, the greater the resources available to soil organisms. Some of the organisms in the soil food web are predators and carnivores on those that feed on plants or decompose plant organic matter. The hope is that by increasing resources to the food web, the numbers of predators and carnivores will increase and be suppressive to the plant-feeding species. That hope is not always realized, however, because the predators and carnivores build up at a slower rate than the plant feeders and are more susceptible to soil disturbance. So, the management may need to be designed with that in mind; no-till may help but herbicides probably won't.
Some soil disturbance is usually involved in growing or incorporating a cover crop. Population levels of some plant-feeding nematodes decline after soil disturbance. Pete Goodell showed that the population levels of root-knot nematode in cotton fields declined about 30% each time the soil was disked during the winter. But, there was no effect below the disked layer; also, what was the effect on soil structure?