That sounds about right, even if undocumented.
No point reacting straight away as otherwise every single 5 minute power cut and reverting to panel battery, or 20 minutes of high current siren ringing elsewhere causing a voltage drop - could cause a low voltage alarm.
I had no end of problems with a similar 'low voltage' feature on a GSM communicator, fitted to a car alarm. It would send the low voltage alarm, not if the car hadn't been used for weeks, which would make sense, but about an hour into each journey, if it was that long... Biazarre. And, no there was no voltage drop! Battery and alternator in A1 condition. Simply turned it off in the end.