I find it very interesting that this ("I can only do things I'm interested in!") theme is consistent among NeFi. I do think it's a Je devt vs Je non-devlt thing.
I think Te looks extrinsically motivated from an Fi perspective but I believe this is a biased perspective. If the Te is sufficiently conscious, its motivations will not be experienced as properly 'extrinsic' to the person. They will be just as important to him/her as Fi interests are to Fi-conscious people.
I find that Te motivations, for me, are not properly extrinsic as long as they are lined up and not in opposition to Fi interests. By themselves they are not gonna be sustained for long. It's like the motivation goes from Fi to animate Te, but Te does not stand on its own two legs... When it gallantly makes the effort, the overall experience/results are a dive towards the unhealthy. Competitiveness, accumulation etc. Temporary but highly damaging, psychologically. Perhaps Te has to do that as it gets conscious as some sort of phase/stage? Idk I don't think these negative experiences are Te perse, more like a dark version of Te/eldar or perhaps an immature Te.
I recently read a book by Alfie Kohn called 'Punished by Rewards', and he talks a lot about the differences between intrinsic vs extrinsic motivation. It was quite paradigm shifting for me. Perhaps I'm thinking of those terms a little differently to the OP though. I think there are external rewards (and internal ones), but I suspect that external rewards are usually sought after for intrinsic reasons. Kohn, at least, makes a great case that we operate much better when going after intrinsically motivated goals, but those goals might look different to different J types, idk. Just thinking out loud...
I think like Aqua said, Te (or Je) looks extrinsically motivated, but I suspect they're still mostly intrinsically motivated, but perhaps for a goal that appears to Ji to be external.