It isn't possible to refresh extracts using Tableau Reader. The Tableau Data Extracts that you send as part of a packaged workbook to people via email, FTP or shared folders aren't linked back to the extracts that are refreshing on your server.
It sounds like the best solution here is for people to log into to Tableau server and view the reports in their web browsers/ipads/tablets,etc. This way the data extracts powering the reports are always fresh as well as ensuring that only authorized people are seeing the information. Business users can also subscribe to Tableau Server views so that every Monday they get an email in their inbox with a link to the view. This way it stays in their inbox workflow, but doesn't cause storage issues like sending big packaged workbooks around can tend to do.
Hope this helps. Let me know if I can answer any additional questions.