Historically, tomcat has never updated the exploded directory when you just drop in a new jar, at least for me. I always assumed this to be a bug, but never looked into it as there is a simple solution. Both of these should work fine:
Deploy the war file using the build-in Manager application. Fine if you are ok with using a GUI for production administration. Note This tool used to have issues if you deployed multiple times (again, I never delved into the details), but a Tomcat restart worked fine.
Stop, Delete, and Drop. Stop Tomcat, delete the exploded directory, drop in the new war file.