Looking at this website it appears that 来てる can have a positive meaning. Is this similar to the instructor telling the instructee that they are "nailing it"?
Your own reference says it’s someone about to be something. In this case, the instructor has just told the instructee to "become a tiger." The instructee growls, indicating some kind of effort to obey. So the sensible interpretation is that the instructor thinks the instructee is on the verge of becoming a tiger. It even works when interpreted literally as the tiger "is coming."
My second question is I am unsure who of You/I/We is being said when the instructor says 体あったまってきたよ is there something obvious that makes it clear who is being referred to?
To me, it’s obvious from the context, the meaning and the lack of an explicit subject change. So before the part in question, you have the instructor saying (roughly) "almost there", and afterward saying "do it one more time" (meaning, try becoming a tiger again). Both of those are clearly directed at the instructee. So, since there’s nothing to indicate otherwise, it stands to reason the part between them is the same. That part means "(one’s) body has gotten warm," which sounds like a physical sign of the instructee’s imminent success in becoming a tiger. Thus the instructor would be referring to the instructee’s body.