The Asco switch sated something like 5 minutes. So the utility power has to be stable for 5 minutes before the transfer switch would switch back. So it would have had your problem covered.it is rare that power goes out. But when it does it has a tendency in that area to come back after a while only to die again after 30-60 seconds and then come back again after a minute or two, this can happen 3-4 times befor it actually stay on. Which is not optimal for switching back and forth fully auto.
You may still want to automate the shutdown even if it's a manual pushbutton. PS: I didn't pay attention to the steps required. Don't remember if the decompression lever was involved.