Your description of Te-Fi is actually Logic
Intelligence Temperament, which is based on cause-and-effect.
Interestingly, the Te-Fi of Ti-Fe users manifests in Backwards-Time and is rooted in the physical dimension (this might allow them to get a feel for things or objects, like how durable or stable they are). Similarly, that Ti-Fe for Te-Fi users is also rooted in the physical dimension, and associated with Backwards-Time (which allows them to get a solution for possible things or objects).
Also, there are no Pi, Pe, Ji, Je, because those J and P dichotomy is dependent on whether a person is introverted or extroverted, and whether the person uses Te-Fi or Fe-Ti. For example, ENTP is extroverted and Ti-Fe user, while ENTJ is extroverted and Te-Fi user. On the other hand, ENFP is extroverted and Fi-Te user, while ENFJ is extroverted and Fe-Ti user.