Autodesk gave us 3 options for Dim text alignment: Horizontal, Aligned with dimension line, and ISO standard. You'll want to use ISO Standard for the dim styles you want to behave as in your example. Keep in mind that if you use rotated viewports, the dimension will be relative to the rotation of the "page north" that was active when and where the dimension was created.
Unfortunately ISO standard isn't dynamic to the view orientation, though it seem like it would be a good fit for that behavior.
Best,
Shannon