It's about angular momentum and happens whenever the axis of rotation differs - even slightly - from the semi-major axis. Interaction with a fluid is not necessary.

You can demonstrate it at home with your smartphone (or, more canonically, a tennis racket), and see for yourself that the tumbling happens much too quickly to be explained by whatever force the air is imparting.

Alright, that makes more sense, the trick is that the (conserved) angular momentum vector need not be parallel with the angular velocity vector, the simplest example being torque-free precession [0]. It doesn't help that most examples of non-constant angular velocity have external forces in the mix to confuse the reader.

[0] https://en.wikipedia.org/wiki/Precession#Torque-free_or_torq...