Calling a promo banner a "prompt" is a bit of an exaggeration. Also, the same "Upgrade to the new Firefox" message is also shown to Firefox versions less than the current version (34).
Using the more general (non-computer) verb "prompt", it just means to "encourage" someone. So saying that Yahoo is prompting (or encouraging) people to switch is by no means an exaggeration.
Edit: removed "upgrade" and replaced it with "switch" as to not imply one is an upgrade over the other. Browser choice is very much a personal preference.