well i tried tweeting @people and i was confused that it didnt show up on their page.
If you go to www.twitter.com
you should see what I just tweeted to you since you follow me.
If you @tweet at someone, it won't show up on their profile page. It will just be added to your page, and since they follow your tweets, they will see it directed at them. Also, you may notice (depending on what version, old or new twitter) that there is a box marked @mentions or @yourusername . In that you will see all the tweets people have made that has @yourusername in it.