The Spotify desktop app absolutely will not stay put on a particular desktop using Mission Control in OS X. It has a tendency to "relocate." For example, I have it pinned to Desktop 3. When I open the app, it goes there. After a while, though, it will move to Desktop 2, and kick the application that's currently there onto Desktop 3. Sometimes (sometimes?) when I'm on Desktop 2 and open Spotify, it will kick the app that's there off and try to put itself on the current desktop (despite being assigned to Desktop 3).
It doesn't matter whether I open the application on a desktop, open Mission Control, and assign it. It doesn't matter if I open it up and try to assign it to "This Desktop" by right-clicking on the icon in the Dock. No matter what I do, it just will not behave.
It doesn't work on Mojave. But it also didn't work on High Sierra, Sierra, or El Capitain either. I have a few Macs, and Spotify (mis)behaves the same way on every single one. And I'm not the first to notice this issue: