By default, Another Number will use your WiFi network for calls and texts which will not impact your mobile bill in anyway.
However, if there is no WiFi network available, the app WILL use your data connection and you CAN also opt to make calls through your mobile phone dialer (which uses your mobile call minutes) when you don't have a good data connection.
As long as you stay within your mobile provider’s call minute and data allowances, you shouldn’t see any additional changes on your bill. When overseas, you may incur additional charges in line with your network’s roaming charges.