You need internet service to initially download the software directly into the target device itself. TheTruthSpy also uses the internet connection to send all captured data to your included web account for review. This is all the SMS, Call History, Photo, keylogger, Notes, Social networking messages, or location information (GPS) you are tracking on the target device.
In case the target device does not have internet connection: Do not worry, you will see the data until it has. So maybe it is delay a little bit because of no internet on target device.