Tbh I think Te is more likely to get caught up in details than Ti. A lot of times with Te-valuers, it feels like they need to walk through each step of something to make sense of it; whereas Ti tends to subsume certain things more quickly. I can see how Ti would seem overly-detailed to Te-valuers, though; in that, it may continue to refine a certain point (semantics, etc.), in an attempt to clarify the "framework," which Te would see as superfluous to the already established external process. But generally, object functions will always feel more detailed to their field counterparts. A good, albeit exaggerated example of this, is Ashton's descriptions of Ne from an Ni standpoint over at socionix. The core idea here, is that object functions diverge and expand, while field functions converge and distill. Just the nature of things.
Keep it real
That seems to be how Te works -- cause—>effect (explicitly). So, it will need to accrue a long enough sequence in order to see how the effects can be subsumed under a more general cause. That is what Ti does -- effects—>cause (explicitly). Observing things and establishing a sense of the unity between logical relationships. So, yeah, Ti will never have any real "direction," because every time you look at a given relationship, it's always in reference to the rest of them; from a Ti agenda perspective, I can say that the need to 'connect' everything in this manner can get redundant and tiring. Especially with Te polr, paying little heed to causal processes occurring ostensibly, it can be as if every piece of information needs to line up with everything else.
And yeah, criteria is a good word. Parameters, etc. If it doesn't fit the criteria, something must be wrong (if a central cause can't be found, we're missing out on some effects). So, it's back to the drawing board, to describe more effects and see how they tie back into a certain cause. Te doesn't care about this, as it is forward-moving and ostensible -- "it's right there" tends to be a common sentiment among them, more so the gammas, since it is paired with Se (localized, explicit magnitudes of objects).
Anyway, it seems that all field functions work backwards, and objects functions forwards, in a way. Fi aligns intentions and relations, making for an implicit sense of the connection between two things/people; Ti establishes parameters; Ni finds a central pattern; and Si secures the base/environment. They all set limits and boundaries on what the object functions can do. Te observes it's gradational processes; Fe tracks causal intentionality; Ne expands on abstractions; and Se breaks up the environment.
Yay for feedback loops.