"He has been very busy since he was back." It seems to me that you're thinking of these two possible meanings: 1. He has been very busy (ever) since he came back. (after an event) 2. He has been very busy because he came back. (because of an event) Most people probably interpret it like #1, because it doesn't make immediate sense for a person to be busy just because "he came back". There should be a clearer way to state it, like "He came back to his busy daily routine", for example. But the bigger problem might be that the original sentence is not very clear for any meaning. The present perfect "has/hasn't been ... (since)" works best with a time point (like date) or an event implying a time point after "since", or "ever since" as is often used for emphasis. "he was back" is more of a state than an event, suggesting "he came back and has been there for an indefinite time (likely up to now, but this part is unclear because of "was")", with a vague sense of duration. So it is confusing the same way "It's been five years since I have learned English" would be ambiguous - does it mean "since I started learning", "since I completed (a major part of) learning", or "since I stopped learning", or what? I recommend writing it like my #1 example if you mean ever since he returned, or phrase it differently if you mean a reason by "since ...".

First, I don’t like “since he was back”. I would write “since he returned/came back”. It’s probably because “since” refers to a point in time and “was back” is not a point in time, it’s a state. At least that’s the way I think about it. Dave Phillips who claims to be a native speaker doesn’t like it either: https://www.englishforums.com/English/ItYearsSinceBackPlease/brjnzq/post.htm I have found examples of “since he was back”, but if you do a Google Books search: “Since he was back” - 17 results “Since he came back” - 55 400 results “Since he returned” - 194 000 results If we change your sentences to: 1. He has been very busy since he returned.” 2. He hasn't been very busy since he returned” Then I interpret them to mean 1. He has been very busy after he returned.” 2. He hasn't been very busy after he returned.” But they are ambiguous. They could also mean he that 1. He has been very busy because he returned.” 2. He hasn't been very busy because he returned” “Using ”since” is often ambiguous because it has two different meanings, but I have never felt it was a problem, because you can always tell from the surrounding context what the meaning is.