You have to distinguish between the display using the card and a given application using it.
With an external card connected, you have to highlight the application in Finder, right click and select “Get Info”. When the Info panel opens, you will be presented with the choice of whether to “prefer” the external card over the integral graphics.
However, even if you choose to prefer the external card, the application will only use it if it is an application that can use external graphics. For example, Compressor will not, regardless of what you select. I gather that the same is true of Illustrator.
The display will use the external card throughout for the purpose of display, but that is not the same thing as a specific application using it.
[doublepost=1554411294][/doublepost]Also, you can see graphically what an application is doing with the external card by opening Activity Monitor > Window > GPU History.