AntiSocial does need a network connection in order to work properly.
There are a few reasons, but the main one is to limit the amount of battery that the app uses to a tiny amount. Any blocking modes that you set, timers and schedules are all pushed to a main server that then calculates if an app should be blocked or not, or how much time you have left.
Also the usage information of your apps is also pushed anonymously to a server and compared to other users for the dashboard.
This means the servers do all the work and calculations and simply feed data to the app on your phone, saving you precious battery and phone resources.