Certified GKH Gardening Expert
Mulching around trees and other plants is always a good idea, especially organic types like pine straw, leaves, etc. When applying mulch around your tree, keep it at least an inch away from the trunk and about 2-4 inches thick.
As for the rubberized mulch, this type of mulch is most often used for play areas and similar locations, as there may be some concern in chemicals leaching into the soil around plants. There are, however, many different types and forms of mulch available. These articles will provide some basic information and help with deciding which type may be best for you and your needs: https://www.gardeningknowhow.com/garden-how-to/info/learn-about-synthetic-mulch-for-your-garden.htm