Here are the things that could cause your situation. Please have the device you provide your child in your hands to check these things.
1. The device you are trying to monitor is not connected to the iCloud account you have setup in your TeenShield account. On the device, go to Settings > iCloud. Verify that the account it says there matches the account you entered for TeenShield.
2. The device has the correct iCloud account, but the iCloud Backup is not turned ON. On the device go to Settings > iCloud > Backup. Make sure iCloud Backup is Turned on. The last backup date it says there should be a recent date. You can tap "Backup Now" here to perform a manual backup. Your TeenShield account should reflect the backup within 24 hours if everything is setup correctly.
3. Apple two-step authentication is turned on for your Apple ID but you haven't contacted us to let us know so we can provide you special instructions.
After you have confirmed everything is setup as above and you have performed a recent backup on the device in Settings > iCloud > Backup > Backup Now, your TeenShield account should start showing the data within 24 hours.