no, archetypes has nothing to do with typology .
first of all extraversion is putting from inside world to outside world(it includes subjective judgments/perceptions to external world) and introversion is taking what is seen irrelevant out of the outside world(this way creating an subjective view of it).
and i think you need to look at J functions too when thinking about P.
but lets first look at S and N like this:
Sensation: Perceiving directly to
conscious what is in the present moment in detailed and concrete manner. "Is there something there/what is?".
Intuition: Perceiving connection between details
which are perceived unconsciously and taken to consciousness indirectly. The connection between things comes to conscious mind, therefore building up big picture perception. Also perceives how things could/might be, and answering to question: "Where did it come from and where is it going?". because it looks at "where something came from and where is it going", its not the perception of the present moment.
but all people use both functions, its just that if N is E, S is I or other way around, and that other function works more unconsciously.
now if you take the fact that E is including and I is excluding. so what do they include or exclude. its the functions in the opposite orientation.
if you think it like this:
Pe feeds info to Ji(which removes irrelevant from it), Ji feeds Pi(which only takes in what is seen necessary), Pi is included to/guiding Je(Pi is creating a subjective bias to Je), Je guides Pe(Pe includes/is guided by Je judgments), Pe feeds Ji and the cycle goes on and on. some types has more conscious Je and less conscious Ji, and pretty much fully unconscious Pe, they all are still contributing to this, you just dont notice it(since they are unconscious)
and when it comes to I/E functions.
with Ni those details(which N connects unconsciously) i mentioned in N description are judgments, memories, perceptions etc. it only connects what is seen relevant. Ni works with Se, so external perception is about details and facts of "what is".
with Si those details are also judgments, memories, perceptions etc. but instead of connecting dots between them, it tells you what is and compares them, based on these judgments, perception, memories etc. also when it comes to Si, external perception of details comes through unconscious(as the external perceptions are from Ne) to Si users, first the irrelevant is taken out and whats left enters the consciousness, is stored there and is able to be directly perceived to consciousness. this leaving out of external perceptions makes an experience that would otherwise be sensuous, making it aesthetic. also comparing memories/judgments/etc to the present moment. with Ne the details(which are connected), are details of external world that are perceived unconsciously.