I have used the below link to @mentioned myself in a chatter post, but the post is not registering in the "to me" section. It is blue and shows up in the "What I Follow Tab, just not the "To Me" tab.
It sounds like you are posting the feed item with an at-mention to yourself. In that case it will not show on the "To Me" feed. However if you post a comment to that feed item and at-mention yourself it would show.
The reason a post created by you will show in "What I Follow" is because you always "follow" yourself.
In the example you show that person is At Mentioning a user that is different than the posting user, which causes the Feed Item to appear in the the "To Me" feed.
If you have more questions please don't hesitate to ask.