Lutron runs completely locally Except for the smartthings integration. Which means rules that you set up in smartthings or if you are using the smartthings app will require the Samsung cloud. But you can use them with their own app locally or with apples’s HomeKit Or a number of other integrations. This is one reason they’re popular: they are a built-in back up system for when the smartthings cloud is down (typically once or twice a month over the last 20 months, but sometimes more than that).
The Leviton Dimmer is officially supported, and I believe it uses the generic Z wave dimmer device type handler, so that is eligible to run locally.
However, it is very important to understand that smartthings itself is primarily a cloud-based platform. I can’t speak to the new “smartthings (Samsung connect) “ app or the new non-groovy platform in this regard (@wb70 or @jkp or @tgauchat May know more), but as far as smartthings classic, nothing runs locally except for the official smartlighting feature and some bits of smarthome monitor. Which means if you set up a “goodbye routine“ to lock your doors and turn off your Leviton switch when you leave the house, that won’t run locally even though the Leviton Dimmer itself is eligible to run locally.
Anything done with webcore will not run locally.
Anything done with a custom smartapp will not run locally.
The mobile app will not be able to communicate with the hub at all unless the cloud is available– – so you won’t be able to toggle that Leviton switch on and off from your phone.
And even a smartlighting automation will only run locally if all of the devices in it are eligible to run locally.
Location.mode Changes will not run locally, so if you have your light switch set to come on in a routine/automation that includes a mode change to “night”, for example, that will not run locally.
Also be aware that when the official supportbase article says “most the wave and zigbee devices that are supported will run locally”, That means devices that are on the official “works with smartthings” list and for which you are not using any custom device type handlers.
(It’s not that there are technical reasons preventing these options from running locally: it’s just how the smartthings multiprotocol platform has been engineered. They wanted to be as flexible as possible and to have many cloud to cloud integrations. When you look at the competitors that do run locally, you will see that most of the requests in their community forums are for more cloud options like IFTTT or Alexa.)
If you’re basing your home automation on Samsung smartthings, you are going to be dependent on the Samsung cloud for most operations. If a locally operating system is essential to you, you should be looking at some of the competitors.