Do I need to restart instances of the JRE to pick up new timezone data?
Yes. Before running the TZupdater tool to update timezone data, you should stop all the relevant instances of the JRE software. Cached instances of timezone data might exist in running JRE software processes if you do not shut down the JRE software before running the tool. Restart the JRE software after the TZupdater tool has completed its work.