Hmmm, never had that happen here. 2 options come to mind:
#1-get the free Sound Radix plugin, Mute-o-Matic and insert after each delay plugin and set to mute on stop(this plugin can be configured to mute at stop, or mute at playback. Mute at playback is handy for automating talkback mics). Build that into your templates
#2-Pull the delay track faders down all the way and save your templates that way(or save with those tracks muted)