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1. If you have set the auto-start property for your project, when you OTA install it, the system will run your auto-start processing as though the application was in pace and the device had just been started. The big difference is that ApplicationManager.inStartUp() will return false, because the device is not in startup. So in addition to running your program at start-up, the auto-start property means it runs on installation too.
2. Honestly I would say that those that need device restart are just being lazy, I can see no reason why you can't do the same things when first run after OTA installation as you can do on device restart. Perhaps those apps do check ApplicationManager.inStartUp and decide they are not in startup mode and so don't want to do the start-up stuff.
Your English is great, I suspect it my explanation that is the problem!