They should be an option to limit your feed only to the people you follow, but it is unlikely we'll see it because it contradicts the platform aim to increase engagement, by hook or by crook.
But in reality, in twitter, like is a soft form of retweeting and users know it. So if someone you follow uses the "like / favorite" feature it also kind of means they want people to see it. For bookmarks, there is a different bookmark functionality. On twitter, like is a low weighted retweet that does not show up in the user's profile directly.
That said, the feature has always worked for me - actually it works too well that I have to think before I use it. Because after setting it once, it seems like I never hear from that person again. So it feels like an unfollow for me. Maybe the functionality depends on how much you interact with the person on Twitter? I don't know. I don't interact with people much on twitter, so when I choose that option, I don't see any likes from that person ever again, and it feels like I see their tweets A LOT less often than desired.
1. Agreement with the tweet, directed at the author only.
2. A form of "bookmarking" tweets for later. It's no accident that for most of Twitter's life this wasn't called a "like" but a "favorite" (with a star instead of a heart symbol).
As for "some of their followers will see it" and "I don't know [how it works]": That is precisely the problem. Your timeline isn't determined by your choices and the choices of the people you follow. The "algorithmic" timeline also adds a lot of randomness and unwanted choices that you can't control.
As far as I can tell, it has never had any effect whatsoever. I still see the components I dismiss, and I still see likes from the same people. Possibly less often... but it's hard to tell when it's every time I open the page.
At this point I click it mostly out of stubbornness and perverse curiosity, to see if the company is at all capable of changing this awful course.
I am generally interested in what they write but on Thursdays they post nudes and like nudes of other females I don't follow, and Twitter shows me a lot of their likes. It annoys me to no end.
You can functionally get the same thing by using the "list" feature instead of following people.