Not sure about dates. It varies by plant and planting zone. You'll need to do some research on that.
As for spring, you commonly would chop-and-drop in place and use it as a mulch to retain moisture and plant into the mulch. You also want to leave the roots in the soil so they can die, break down and feed the worms. You should also do this with your garden plants- leave the roots when possible. The mulch will also break down and provide natural nutrients to the garden.
The technique is a form or organic gardening which builds up organic matter in your soil, helps to loosen the soil and provides nutrients for the life in the soil- worms, fungus, bacteria, etc. Those in turn convert the organic matter into forms that your garden will be able to better utilize. Over a number of years, this cycle can build to allow for amazing results, but it isn't an instant solution.
If you do use these techniques, then I recommend that you do no additional rototilling. That will break up and kill a lot of the under-soil life. Some hand tilling to break up chunks of soil and loosen weeds is fine.