It sounds like it could be another app, or it could be remnants of that app get left on the device. Almost sounds like malware or even a virus. I would first get yourself the necessary apps to check for malware and viruses on the tablet. Then I would try booting the device in "Safe Mode" and see if you can uninstall the app from in there and run the other stuff to check the system. Once done, restart the phone to get out of "Safe Mode" and see if things are good. If not... worst case... you may have to back up all your personal stuff from that tablet onto a computer and then do a "Hard Reset" of the tablet, wiping all on it and starting over.
To get into "Safe Mode" please do the following.
1. First turn off the tablet.
2. Next press and hold "Power" until you see the manufacturers logo on the screen, then release the power button.
3. "Quickly" press "Volume Down" and hold it for few seconds until you see the message "Safe mode: ON" or something similar.
4. If you wanted disable it, simply repeat the steps above, and you should see "Safe Mode: OFF" rather than on.