It should work. It's hard to say more without more information. Although I think there's an iOS issue where the app icon is cached the first time so won't be updated. So if you exported with the default icon, tested it, then changed the icon and exported again, iOS will keep showing the old icon. I think you have to uninstall the app, reboot the device, then reinstall the app, to get the icon to update (or something like that).
Regarding the icons, I kept the same "object", just redraw it over the default icon. I have checked that the purpose of each is "App icon".
I have exported in Xcode the project, and have seen than on the exported files, the default icons are still the old one....