Yes, I figured it out, that every additional call of Update() function, causes that mesh is moving faster along the path.
Wow. I didn't know TVMesh.Update causes the path speed to speed up. That means you can't even use TVMesh.SetMatrix to correct the mesh to where it's supposed to be. Also if you modify the mesh's position/orientation/scale in any way multiple times, that kinda makes tvpath unusable.
With position the problem doesn't occur. Only with rotation. You can Get/Set a position and the mesh is moving normally. But when you want to do something with rotation it is speeding up.
I have found a half-baked work-around. Any time you are planning on doing anything with the mesh, set the path to null first. Then when your done, reset the path. It's not a general solution you have to know what TVPath object to set to that TVMesh, and it's properties ahead of time. There is no TVMesh.GetPath or TVMesh.GetPathProperties so the work-around breaks OOP rules.
I'll try that. Thanks.
Not everyone is strictly following OOP rules

There are often situations where you can break them down, because it'll speed up coding or will just simplify certain things. Nothing wrong with that.