Twitter's default view is an algorithmic timeline which in addition to being ordered randomly (you can't easily tell whether you've reached the end, thus spend more time on it and more opportunities to see ads - I believe this was the original reason why all social platforms switched to this model), it will also include tweets from people you don't follow.
You can opt-out and go back to the chronological feed (not sure if that also includes tweets from people you don't follow) but the setting "accidentally" resets every so often.
"Engagement" also goes beyond ads that you see. If you "engage", despite not seeing ads yourself, you're still contributing to their DAU/MAU metrics and creating content that others might engage with and they might see ads.
