Unless your tag is so commonly used that it is among the top five tags for a thread, you are the only one who will see it. In fact, when i tagged this thread Science, it was the first time that i had ever used that tag. However, i knew it was such a commonly used tag, that it would supercede almost all other tags. So your tags would only overtake the other tags for a thread if you had used them so commonly that they were more frequently used than the other tags which had been applied. For example, when i see the pro-Russian or anti-whoever the Russians consider enemies threads, i tag them "Russian Propaganda." I've tagged do many threads with that tag, that it usually becomes the number tag for such a thread.
How commonly a tag has been used throughout the history of the site is the criterion which establishes whether or not it becomes one of the top five tags for that particular thread. If it does become one of the top five tags, everyone will see it.