You can change how the Texecom dialler responds, at default its code or restore, but you can change it to retore only or code only or nothing.
On Nothing once its started the process it wont stop, even if the trigger has been restored until ts gone through the motions, you can get it to dial everyone, by changing the acknowledgement type.
Acknowledge only, will stop calling the person that has acknowledged the call and dial the next in the list when the call is ackwnoledged (texts are automatically acknowledged), Stop calls will stop the system from dialling anyone else once a call has been acknowledged by anyone in the system.
I think its better to have it on nothing and stop calls (unless using text), so that someone that acknowledges the call is the one that deals with the problem and it doesnt dial anyone else and it doesn't matter if the bell timer is on for a short time.
Depends on what you can do easily at the panel end I guess, but the dialler is very flexible.