Well the avast process has found ZA and it is usually able to determine if it is the Free or Pro version, I suspect that even though you got the free offer or free today, it would normally be associated with the Pro version of ZA, so that may be why the avast!/ZA dialogue pop-up window was displayed.
The main need for the disablement of the avast Web Shield Transparent Mode Proxy if if the version of ZA includes a Privacy mode function, this is usually in the firewall and I don't know if this also comes with or you have ZA firewall.
If there is no privacy function you can enable the avast Web Shield Transparent Mode Proxy again.
Use a text editor and edit the avast4.ini file, the default installation location is C:\Program Files\Alwil Software\Avast4\DATA\avast4.ini (I would advise you copy avast4.ini before editing it, just in case).
If you answered incorrectly, Locate the line containing ZoneAlarmCompatibility= and delete that line (avast will ask again on reboot, answer NO) or change the value to =0. Save the edited avast4.ini file.