I think you can always arrive at the correct answer by tracking the distance traveled by the center of the rolling object.

In the original SAT question, the center of the rolling circle is 4r from the center. That means it travels an arc of 8pi. Then assuming no-slip, that works out to 4 rotation.

In your case, rolling on the inside, the center of the rolling circle will only be 2r from the center. Using the same logic, this yields 2 rotations.