I hope you were not too badly affected. Such a tragedy.
The SmartThings platform is cloud-based. Very few automations run locally, really just the official smart lights feature. And, as you noticed, no notifications run locally and the app cannot talk to the hub even if they are on the same LAN. That has to go through the cloud as well. People buy smartthings for versatility, not for local control.
https://support.smartthings.com/hc/en-us/articles/209979766-Local-processing
There are a number of competitors that do run primarily locally, so it really depends on exactly what you’re looking for. And everybody has their own opinions.
If you want something solid and stable, but with many fewer Options in both devices and rules logic, and you already use iOS devices, apple’s HomeKit is a good choice. Everything runs locally except voice control, and you can use Siri over cellular if needed. I use this in my own home. ( i’m quadriparetic, so reliability is very important to me.) There is an article in the community—created wiki on devices that work with both smartthings and HomeKit. There aren’t many, but there are some.
http://thingsthataresmart.wiki/index.php?title=Devices_that_Work_with_HomeKit_and_SmartThings
If you have a strong technical background, some of smartthings’ former power users started a tiny company last year, Hubitat, Which sells a hub that does Much of what smartthings does, with most of the same devices, But runs everything locally. Except for third-party integrations. They are good people with strong skillsets, but again, very tiny company just getting started. Quite a few people with strong technical backgrounds looking for local control have added it to their smartthings systems. However, it has no app at all yet. They assume that everything is going to run based on rules that you set up, although there is an echo integration as well- – but of course that is cloud-based. So I don’t know if it matches what you’re looking for.
See the following thread for more discussion
https://community.smartthings.com/t/hubitat-elevation-hub-home-automation-that-is-local/117107
Other than that, you have quite a few options, but they will almost all cost more than SmartThings, so that’s another consideration. Insteon is decent, And tends to have a high family acceptance factor (FAF), just not quite as modern as some of the others. And they are using their own proprietary communications protocol, so you can’t reuse most of your other devices. Homeseer is very powerful But works primarily with Z wave devices. No zigbee. But you have to be pretty technical to use it, it’s nowhere near as consumer-friendly as HomeKit or Insteon.
Every system has pluses and minuses. So it really depends on what you yourself prefer. And of course on your budget.
There are probably a dozen threads in the forum discussing various local processing alternatives. And again, everybody has their own opinions. Here’s one recent one: