If you have a smartthings hub, then you would use smartthings to manage the scenes based on the button presses on the scene controller.
There are community members who have used that particular Leviton device with SmartThings successfully. But it is one of the more expensive options.
The following two threads should be of interest to you. Again, these will assume that you have a SmartThings Hub, and that you will set up the groups and rules with that. ( these are clickable links)
