keep at least 2-3 feet away from the tap root, and then go to town! It will keep out weeds, but water it heavily and keep it from drying up and heating up. Some woods have natural chemicals that you need to be aware of before mulching. Eucalyptus keeps away insects, Ironwood and other pine needles kill grass. The quicker the mulch breaks down the better it is for your trees. It is very good to expand on what you are doing with the mulch, check the PH and add 46-0-0 if necessary. Add dirt to the mulch and work it in every month turning it over. Turn some into biochar, or just burn some in a 'sawdust stove' and use the ash to work in as fertilizer. Mulch heavily, then remove it all add dirt, then remulch. All in all the microorganisms will break up your soil, but just be careful it doesn't kill your trees.
Also some trees have berries and other things that aren't edible but would provide a great breeding ground for gnats and flies, especially heat will help to breed gnats. Flooding the mulch will help with that.
Or just turn it into compost, pile it high, add grass, leaves, manure, and cover it. Till it and work it together every month and water it as much as possible. Although this is the most time consuming, after a few months you will have a more quality mulch that is safer to apply to trees.