No, you don't have to. If your phone has WiFi and you don't need the real time tracking, you can run this GPS tracking app as WiFi-Only mode. In this mode, this GPS tracking app records location and saves to the device storage. When the device has a WiFi connection, it then uploads the data to the server. Since the device does not have a constant data connection, you will not see the up-to-date location on your map page until it has a WiFi connection.
If you need to monitor location real time, then cellular data service is required. Cellular data service enables this GPS tracking app to upload location as soon as it is recorded.
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How the FollowMee GPS tracker app works?
How much data does this FollowMee mobile app use?