How should I respond to a reviewer comment that I didn't make changes when I did?
Treat it as a mistake.  

It sounds like the reviewer may be looking at the old version of the manuscript, either due to their own mistake or someone else's.  Alternatively, the reviewer might not have noticed the changes (which sound somewhat minor).

You should assume the reviewer is simply mistaken and respond with that in mind.  Something like:


  Sorry, there seems to be a misunderstanding.  I did indeed update the paper with changes in response to the reviewer's request...


Did you also include a point-by-point response to the reviewer?

From the situation you describe, it sounds like you may not have.  Even if you agree and make the changes, you should still say so, and state what you have done.  For example:


  The references list needs to be updated. There are old references
  (1980s – 1990s) that can be replaced with more recent ones. Please see
  below a number of suggested recent papers that can replace old
  references. If the authors are not willing to omit old references at
  least can use them together with more recent ones.
  
  We have added several more recent references.  Thanks for the suggested papers.


This should remove the possibility of such a misunderstanding occurring.  

If you did not do so initially, include it now when you respond to the reviewer's objection (and I would apologize for not making the changes clear in the first place).