On V2 of the app the lights are configurable for 'on' after power loss. There's 'Last status' and there's 'WiZclick' that lets you set 2 different modes.
I don't use any physical buttons to control my lights (porch fixture with 3 candle bulbs). But I do use virtual buttons. I set up a virtual button device with 6 buttons. Then I program 'push' actions for the 6 buttons in Button Controller. I 'push' those buttons in scheduling apps. This is conceptually the same as using a dimmer in 'smart bulb' mode. The only difference is how the buttons are pushed.
Here is how my Button Controller app is set up:
This process performs fine for me. Sometimes 1 of the 3 bulbs come on a couple seconds after the others, I attribute that to bad WiFi signal on the porch or some other Wiz issue. But that's the only issue.
So I think you are back to turning on logs and identifying where unexpected delays show themselves.
