I use the Nostur app (client) it is also for iOS. In settings you can limit the events you see to those signed by your follows( Web of Trust filter set to Strict) And you can make a feed specifically from just a subset of your follows you want in it. You can turn all the other feeds off (that show you trending notes, etc) Other than that to see only what your follows post and no more, make sure you aren’t following any hashtags. That is the typical way of seeing people you don’t strictly follow. Nostur shows replies and notes in the same timeline feed. So that may be different than you want.

But whether it’s Damus or Nostur a note from someone you don’t follow is probably a hashtag you do follow or a repost of someone you follow.