Question
Will Dichlobenil placed on top of the ground near a Magnolia tree (before installing a hot tub to keep from growing up between the pavers )kill the tree or injure it?

Answer
No the Dichobenil will not harm the tree. BUT if more than 1/4 to 1/3 of the roots are damaged the tree will show signs of branch and foliage die back. The weight of the tub will cause compaction of the roots and may  kill the roots under the tub counting for the 1/3 root damage. Also magnolia trees have a habit of dropping leaves throughout the year and you will get leaves in the tub to contend with. Also be careful when draining the tub that the water with the chemicals goes away from the tree this can damage the root.