It’s true that in general smart bulbs will come on bright when power is restored. There are a few exceptions where previous state is stored in the bulb. That’s considered a feature, because the manufacturer assumption is that the bulb will never lose power unless there was an unintended power outage. So it may depend on the exact brand and model.
The question of the app is complicated because some specific bulb models will send a message to the hub when power is restored and others will not. So in SmartThings it varies how quickly the app will catch up with a physical change at the switch if it is not a smart switch. So for that reason there’s no one single answer, it might be that you would see a similar problem with SmartThings. What’s the brand and model of the bulbs?
One more thing–If you currently have a practice of frequently turning the light off by actually cutting current to it, I recommend that you not do that. (And if you check the user manual you’ll see the manufacturer does as well.) That practice can significantly cut the life of the radio in the bulb because of the inrush current each time the switch restores the power. So you’re better off adding a smart control to those rooms.
The good news is that with SmartThings you will have many more device choices than you had with Iris, including some specifically made for the control of smart bulbs . 