In fact you have tetrahedral elements touching side to side everywhere. There is nothing here to worry about. SolidWorks uses quadratic tetrahedra, which have nodes at the corners and at the midpoint of each side, and which use quadratic shape functions. The actual requirement for compatible mesh is that you have node-to-node--nodes are shared between elements. So you could, I'm pretty sure, have corner to midpoint touching with no problem. But if you look closer at your mesh, this is not even occurring. In every case, it's corner to corner, side to side.
i'm not sure i understand what you think is wrong. you have transitions between 2 different element sizes, the software needs to do something to account for that and in this case it needs to "fill in the gaps" with elements of different sizes so it doesn't exactly match.