The circuit board inside the device has some play, but perhaps that is normal? It seemed to only be generating the tamper when I open and closed the door before, but now it seems to generate completely spontaneous tamper alerts.
If you could pretty commonly cause it to occur by some vibration of the sensor (opening and closing the door) then the switch is almost certainly not firmly closed for whatever reason. If loose enough inside the tamper switch may be pressed barely enough to close and may open intermittently.
The QS1115-840 uses a tamper switch which is depressed not by the front cover, but by the back of the housing. Did you screw down the back-plate to the door/frame? The screw hole is optional and is used as a break-away tamper, so that if someone pries the sensor from the door without removing the cover, the piece that closes the tamper switch is broken off and a tamper alert goes off.
Be sure the break-away portion is not loose or partially snapped off.