Basic: What drives the time-based scenes?

What I mean by that is in trying to understand where the "brains" are for all the scenes. Is it all driven and controlled by my phone or is anything whatsoever stored at the light? Why? Well, what happens when I travel and am outside of Internet reach? Will my lights suddenly stop turning on at sunset and will Smart Away fail? If so, that's a HUGE concern.

The Smart Bridge controls everything. It's a small networked box that is permanently attached to your home network. Your phone controls your lights through this component. This is also what allows you to control your lights when you are not at your home.