Does a recommender need information about my current job?
Yes, it's normal and very good for him to have this information.

Think about it.  Which of the following letters (slightly exaggerated) seems stronger?


  I was Adamia's PhD supervisor.  She wrote her dissertation on XYZ and obtained nice results on P, Q and R. Since then she has been a postdoc at ABC.  I have no idea what she's doing there and I really don't care, it's probably not that interesting.


It shows that you used to be doing good work, but doesn't establish a continuing record.  Compare with:


  I was Adamia's PhD supervisor.  She wrote her dissertation on XYZ and obtained nice results on P, Q and R. Since then she has been a postdoc at ABC, where she has been working on J, K and L, and published two papers in top journals.


If he can address your current work in your letter, he can assert with more conviction that you have an ongoing pattern of success that is likely to continue into a new job.