Try enabling another theme and going to Appearance > Customize.
I did this last time and no settings/options appear.
So the issue is not related to Integral Pro.
It seems it’s an issue with WP itself.
We have tested Integral Pro with WP v4.7 and it works fine.
I honestly don’t know what else you can test without knowing more details about your environment.
You can try installing Integral Pro on another WP site you have on your server to see if the problem persists.