First, I assume you mean one of the
perceiving functions and one of the
judging functions.
Second, Jung didn't believe "introvert and extravert" were "flipped" between the dominant and auxiliary functions. He thought the same "conscious attitude" applied to both the dominant function
and — to the extent that a second function was differentiated and became "a co-determining influence" in the subject's "consciousness" — the auxiliary function, and you can read more about that in
this post and the post that follows it.
Jung's function stack for a Ti-dom with an N-aux was Ti-Ni-Se-Fe.
Myers flipped the attitude of the aux (while admitting that was contrary to the view of almost all Jung scholars), so her function stack was Ti-Ne-Se-Fe.
A true nobody named Harold Grant subsequently flipped the attitude of the tertiary, leading to the Ti-Ne-Si-Fe function stack later adopted by most of the 90s cognitive functions featherweights (e.g., Berens and Nardi) and beloved by hordes of bamboozled internet forumites.
I hope this clears things up.