you must have a species of trees that have shallow roots. Many trees have either shallow roots or deep roots.
for example a few trees that I know of that are shallow: All the talow trees, all the weeping willows, except for corkscrew, some bradford pear trees, and in general short lived trees have shallow roots.
Deep rooted trees, oaks, pecans, maples, and the such.
If you increase the dirt around these trees they will just rise up higher, but your taking a chance of killing the tree. If the soil is too high above where the soil is now, the tree will die.
I had a weeper that had too high roots and it actually ruined a good lawn mower by shearing a pin so to speak, anyway, I got an ax and severed some of the larger roots and this worked. They have soo many roots that one or two or three makes no difference.
Some times trees will send up feeder roots in time of droughts and water shortages to seek water where ever it is. If you are watering your lawn alot and there has not been much deep soaking rains, the trees are going up to get that grass water. In times of plenty of water even a shallow rooted tree will go deep for water.
Trees are really a magnificent manufacturer of water and will seek it out desperately. I know that a mature pecan will require around 300 gallons of water a day in the hot summer. They have to supply the leaves and branches with much water. When water is scarce, they drop off leaves to compensate for lack of water and maintain by cutting back on folliage.