Vinca minor likes partial sun to shady areas, so under the tree sounds like a good location, but it likes rich, well-drained soil, which isn't always the case for typical Texas topsoil. How is your yard managed vis a vis watering, fertilizing, and hours of sun on the vinca bed?
In some areas this plant is considered invasive, so it may be a good thing that it has to struggle a bit in your area. You're less likely to have to chop it out at some point in the future.
I would suggest working in a mix of compost and soil amendments (greensand, lava sand) and improve the soil in that bed. Be careful not to cover the root flare of the tree. This is essentially a modified version of the sick tree treatment (you wouldn't need to spray the tree, but aerate the soil around it, apply amendments, etc.).
