While it's true that people follow their affirming media (e.g. Tucker Carlson), they also accept a lot of what he says, without critical thought.
The "facts" he presents are the basis for their beliefs, and since he is very selective and slanted about the information he presents, they believe it to be further affirmation of their preexisting beliefs or biases.
This is the essence of propaganda and manipulation. Fill in the gaps of people's knowledge/belief with something that's plausible and favorable to you, even if it's only part of the story.
Content generation is Propaganda 101. Editorial control of a trusted entity is a higher level. Algorithm manipulation of a (perceived) neutral/noninvolved source is a higher level yet. And personalized algorithm manipulation is basically spear phishing. Which works extremely well!
Contrast this against the NYTimes. People follow it for the woke, pro-hegemony, pro-establishment stuff. But as per the example with Senator Tom Cotton, if they veer to far from this ideology, far from just accepting it - they rant and rave, and if NYTimes didn't promise to get back on track - they would also have left.
People pick their worldview and biases, and media (in current times) sees it as their role to deliver on those biases. When they don't - the audience leaves and moves on to somebody who will.