i also use zonealarm on 1 of my computers. i noticed during installation setup there are certain settings you can select to allow zonealarm to protect your computer automatically in the background or alert you each time something happens. maybe during setup you may have chosen that particular option. if you did, then zonealarm wouldnt alert as much.

i tried grc.com tests ... zonealarm blocked (stealth) on everything, yet i didnt get any alerts.