So, as others have noted, they do not require an internet connection to run, and as long as they are powered, they will continue to run their set schedule. The one area it might get dicey in a power outage situation is that I would assume some minor interruption in power as the generator / UPS switches over. When the lights come back on, They would attempt to establish connection to the wifi again to get time sync information from it, so if your wifi is not on the same generator / UPS, and doesn't come back, the lights would not know what time it is, and the schedule might be off as a result. This is where the owner
@danlu_gt might be able to address if my assumption is correct.
As others have noted, the web interface for programming is so good, I also don't miss the controller integration I had with the Radions I replaced. The only area I might like to have that would be for switching to a low-power mode in the event of a power outage, as I don't have a generator, only a large battery backup / inverter that will drain pretty quickly if these lights are at or near full power in an outage. Right now, they're on an outlet that's not backed up, so my tank will be dark until full power is restored.