Hello,
I've installed OnlineFamily on my Nexus 5 with android 4.4, and its blocks properly restricted sites on the Chrome default browser on the Nexus), but when i'm using private browsing - its blocks nothing! At all. No alerts in the logs, no blocks on mobile phone.
Installed last version of the OnlineFamily from december 10, 2013 (are you planning to upgrade the soft on android?).