Ask Mr. Smarty Plants

The Lady Bird Johnson Wildflower Center, home of Mr. Smarty Plants. recommends only plants native not only to North America (excluding Mexico) but to those areas in which the plants will be grown; in your case St. Johns County on the northeastern Florida coast.  Ruellia brittonia (Mexican petunia) is native to, well, Mexico. Since you live in Florida you should read the following two articles:

Floridata Ruellia brittoniana, see the Warning at the bottom of the article.

Florida Invasive Plant Education

We just learned that petunias are considered to exhibit allelopathy, as well as oaks. Allelopathy is the release of chemicals by the plant which discourages competition from other plants. Maybe the oak and petunia would duke it out, but we are rooting for the tree.

Please note that it is difficult to impossible to grow anything under any tree, including grass, because of the needs of the tree roots for moisture and nutrients from the soil and because of the shade from the tree. Here in Texas, we would vote for the trees and spread mulch under the shade of the tree. See our How-To Article Under Cover with Mulch.