That is the expected behavior of a reverse proxy, what you are looking for is a redirect. There are a few different ways to acheive this that are covered in this blog post.
Probably here is an example using the return directive that should work for what you are looking for:
Now this is very simple and would send any request to that subdomain to the specific URI, so any paths that were included(ie resume.my.site/foo) would end up at my.site/resume. This is probably file for this usecase, but may not be ideal for others.
sorry about that, I misread your post. That config looks like it should do what you are expecting. Is there anything in the log files? It might also help to share the full config instead of the 1 location block.