This has not been my experience. I have used Primal Web, Primal iOS App, Nostur iOS app, Damus iOS and macOS app, and Iris Web
Discussion
There's a remote chance that one of the apps didn't read your relays properly.
Primal is an exception - it uses a caching system for reading notes, so it ignores your relay list for getting notes. But what notes you see on Damus, Nostur & Iris on your home (i.e. Following Feed) should be the same.