Does "Wi-Fi Assist" respect rules about which apps can use cellular data?
I have tested this with my own app and home server (plus my horrid internet at one part of my house). I created an application that sends an HTTP request to the server when you press a button and an application on my server that makes a sound when it receives it and records the IP address.

When the app was allowed to use cellular data, it went through quickly and had an external IP (confirming the request went through cellular).
When it was not allowed to use cellular data, it tried to use Wi-Fi and eventually did send the request (after some time), using a local IP address.

So Wi-Fi assist does respect the rules that you have set in your phone's settings.