I have several Sylvania smartbulbs, and all but one are outside, set to go on and of at certain times. One however it inside the house. The other day, I lost my WiFi in the house due to an outage with my service provider. during that time, I was unable to control these lights at all. The one’s outside weren’t an issue, since it was night and they were on, but the one inside I couldn’t control with the ST app. I thought that with no internet to the house, I was still supposed to be able to control bulbs locally, and I thought I had in the past. Any ideas what’s going on?
Control through the app never works when the internet is out (and never has) even if your phone is on the same Wi-Fi as your hub. App messages go to the smartthings cloud and then use the Internet to come back to the hub. They didn’t have to design it that way, but they did. 
If the Internet is out, then automations which you have previously created through the smartlighting feature in the app Which use only devices which are eligible to run locally can still operate. But only those automations. And you cannot create any new automations while the Internet is out.
https://support.smartthings.com/hc/en-us/articles/209979766-Local-processing
So if you already had an automation to turn your lights on at 6 PM, or so that when you turned on a specific switch which was eligible to run locally, then those might be able to work when the Internet is out. But app control does not.
SmartThings is still primarily a cloud-based system. They have been promising more local processing for about five years now, but so far, The smart lighting feature is all there is.
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I just realized what I’m thinking of. I have a couple SmartThings buttons, which those locally process if they are controlling something in the smart lights app.
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