When you rotate a model past 180 degrees, upside down, mouse rotation in the left and right direction gets swapped resulting in the model rotating right when you drag the model left.
This is a behavior of the ‘Turntable’ style manipulation model that is the default in the Camera Manipulator. The Turntable model is intended for viewing of models where the ‘up’ direction is important. e.g. looking at a building model. For some part viewers, the the other manipulation models might be more relevant.
The Camera Manipulator provides a collection of different models, and you can check them all out in the live demos on this page of the docs:
Yes, I see the Trackball style control is what I am after.