Is it okay to reproduce the work as a teaching assistant?
I agree with user11388 that it would be good to &quot;cite&quot; the video you used, but otherwise I wouldn't worry much about this. Truth be told that most of us in academia, in the early part of our teaching career, &quot;emulated&quot; the teaching of our own teachers, especially the ones we most admired. Over time you learn to be more spontaneous, but at the start you try to follow a good model. It is partly what mentoring is about.
However, you will &quot;add value&quot; to the lecture just by being there to answer questions that might arise and to (hopefully) watch the student's reactions so that you can notice difficulties of comprehension.