I agree about the wiring. If the alarm is not seizing the line, causing people to hear the alarm calling out to the station, it sounds like it's not wired for priority/line seizure over the other jacks in the house.
From my training/experience, alarms are supposed to be wired like this:
Phone line from outside ---> Alarm "in" (red/green pair)
Phone jacks from inside ---> Alarm "out" (black/yellow) *Better to have each jack terminated on a block instead of all the pairs twisted together.
This is so that the alarm cuts off the phone jacks in an alarm situation so that someone can't just pick up the phone and prevent the alarm from dialing out.
I don't know too much about alarms, but it seems to me that alarm control panels check for dial tone (or at least phone line voltage) every so often (5 or 10 minutes?) and if it goes away, most systems make the keypad beep to indicate trouble.
I've personally experienced this with another phone company's service in the MIDDLE OF THE NIGHT on 2 different occasions
But anyway! If the system is armed, it may (or should?) even set off the siren.
Sorry if that's a little long.