Here's my attempt. I didn't see any way to improve the Te-base description, not surprisingly.
Mostly I filled out the Ti-Ego ones, from my own experience with the two.
Ti-base is focused very heavily on what does and does not make sense. They are always aware of whether things fit together logically or not, and they are skilled at following a logical train of thought and coming to a logically accurate conclusion. They are well aware of the practical workings of the world and often refer to it in order to get more information from which more conclusions can be built. They feel little need to interact with the world though. They can much more easily learn about reality through reflection and conclusion building. They can be prone to dismissing evidence that contradicts their logical conclusions, because there are always exceptions to the rules. Often they will try to reclassify the contradictory fact in order to explain why it was an outlier. Unless enough external evidence is shown to prove something to be incorrect, they won't let go of guidelines that represent how reality is at least most of the time, and even then they prefer to understand the logical reason they were wrong before accepting the evidence.
Te-Creative are focused on causal functioning of the world. But, they spend less time directly involved with the world unlike Te-base. They spend more time observing the processes taking place and they begin to build an understanding of how it works. They also become aware of the various explanations behind why the world is the way it is. When they do interact with their environment they are guided by how they understand what they are interacting with. However, they know the limitations of logical analysis and will quickly let go of explanations which they cannot rely on when interacting with the world. For them, evidence always trumps explanations.
Ti-Creative are focused on how they understand the world. They build and deconstruct understandings very often and quickly. They like the exercise of discovering new ways of explaining the world, but they are not concerned with maintaining all-encompassing systems the way Ti-base is. While they enjoy coming up with new insights into why the world is the way it is, they are also always aware of the empirical evidence of how the world actually works, and take note when their explanations are not supported by facts. Contrary evidence causes them to question their logical analysis sooner than Te-base, and they will freely adopt new explanations if they can find them. They find themselves deriving new patterns and ideas from processes occurring in the world, and this is because they are continually subconsciously taking note of all the ways in which the world functions. However, they are aware that there is more to the world than just the observable workings of it, and consequently they feel free to follow logical trains of thought beyond what fact and evidence can prove.