Why does someone else's notifications come up on my Twitter account for iPhone?
In a nutshell - your phone asked to be notified and never cleaned up that request (or the clean up request didn't get processed correctly.)

If you simply uninstall the application and wait (perhaps using a different iOS twitter app in the meantime), the system will remove your device from that notification queue once it misses enough deliveries of a notification. This takes a variable amount of time, so you might want to force the issue by logging back in as your friend and removing the request to send notifications to your iPhone.

According to this thread on the Apple support forums, here’s that fix:


Log in with the previous account in Twitter settings.
Go to the Twitter apps’s “accounts” page.
Click “Settings” (bottom left).
Edit the notifications of the previous account by switching to “off” for “mentions and replies” and “message”.
Finally, delete the account again.