For Android lang, good thing open source sya and may PRO version. Guaranteed hindi nag ph phone home yung app.
For iOS, not allowed pero pag jailbreaked meron app for that I forgot the name parang Firewall iP which you could get sa Cydia
Eto example screenshot i did just now, makikita connection ni Viber, at si Fit connecting to the internet. You have option to enable connection to internet only when app is active/screen is on. so pag background pd nd sya dapat maka connect sa internet