Your question is a bit of a confusion to me but I think you want to know how it is that on your timeline, you're seeing all your followings tweets. Correct?
Well, if you entered www.twitter.com/{your username}
into the web browser's address bar, you should see all your tweets alone.
When you go to the homepage of Twitter, after logging in, you will see tweets from the people that you're following.
So you said, “I follow people, I get all their tweets in my timeline.”—If you checked the URL of that page, it would probably be the homepage of Twitter. Which, after logging in, shows your timeline (and NOT your profile).
And, “I have been to other people's pages and I can see only what they have tweeted in their timeline but they are following people.”—Check the URL, you should probably see www.twitter.com/{their username}
. It's their profile that you're viewing.
They can follow any amount of people, but when you go to their profile page, which is www.twitter.com/{their username}
, you'd only see their tweets and retweets (retweets are tweets from other people tweeted by this person).
It's how Twitter works.