The feed at the top right of Facebook (the sidebar) is not limited to posts that will appear in your newsfeed; it also includes your friends’ interactions with their friends, who might not be people who you are friends with. Likewise, your interactions with all of your friends will appear on your friends’ sidebars. Some people don’t like having quite so much of their Facebook activity declared to their friends, so you’ll frequently see some variation of this post:
“Please do me this favor: Hover over my name above. In a few seconds you’ll see a box that says “Subscribed”. Hover over that, then go to “Comments and Likes” and please unclick it. That will stop all my posts showing up on the side bar for strangers to see. If you repost this I will do the same for you. You’ll know I’ve acknowledged you, because if you tell me that you’ve done it, I’ll “like” it.”
Sometimes these requests are full of misinformation (e.g., “strangers” can’t see your posts in their newsfeeds, although strangers can see their friends’ posts on your wall, partly depending on your permissions). Regardless, you can’t control what shows up in your friends’ sidebar, only they can. So whether or not they choose to do as you request is entirely up to them.
All of this is to say that the “thanks for the add” post by your new friend (let’s call him Frank) would have appeared in the sidebars of all of Frank’s friends, unless they clicked “unsubscribe” for Frank. It would not have appeared in your friends’ sidebars, though it would have appeared in their newsfeeds (centre of the page). So, even if you’d sent out one of those “please unsubscribe from me” status updates, and even if all your friends unsubscribed from you, you could not have prevented that post from appearing in Frank’s friends’ sidebar.
I wouldn’t consider it stalking for someone you don’t know to notice it.
Good question. I get the feeling a lot of people don’t know how what the sidebar is doing.