Avast can "change itself". Avast has internal security checks at startup and if something does not seem right to avast it will, as I understand it, try to revert components back to something it does like and, potentially, try to go out to get a clean version.
That's why when we get one off updates from avast they are accompanied by a .sum file to prevent avast from reverting the updated component at the next restart.
So, it is just possible that ZoneAlarm, far from being the problem, is just doing what it is supposed to do, noticing that avast has changed and asking for updated permission.
Let's remember that the change you made to your system was to reinstall avast not ZoneAlarm.
Have you tried an uninstall and fresh install of avast?
Does the problem still exist if you go back to version 691?