The best way for me to explain this is for you to take a look at where your applications are running.
Login to the IDE–>click “My Locations”–>Click on the name of your location–>scroll down then click “List Smartapps”
Apps showing as “Cloud” do not function when there is an internet outage or the Cloud (your execution Shard) fails.
Now on the top menu click “My Devices”. Devices showing “Cloud” in column Execution Location do not function when there is an internet outage or the Cloud (your execution Shard) fails.
Also the ST Phone App communicates with the cloud which then communicates with the Hub, so during an outage it may not be possible to arm/disarm your system. That is the reality of using a non-ADT Smartthings system. In my case I had no security system so I’m OK having a system that works 99.something percent of the time, without a large financial outlay, and no monthly monitoring charges.
One method of mitigating the internet outage issue is using a Router with CellPhone backup that has battery backup or is plugged into a UPS.
For more information search this site for “Local vs Cloud” and check out this thread
@JDRoberts if I’ve missed something or you have additional information, please feel free to respond.