If my Twitter handle were @johnsmith, and I were to change it to @johndoe, I'd expect that searches in the Twitter search input for the old username would now show no connection to the new name.
On the contrary, if I change my handle, wait a few days, and then search the old name, I see the many replies from other users tweeted to the old name, and some of these—but strangely not all—have the new name added to them now (they show as tweeted to both the old and new name, despite being dated before the new name existed).
Why would this be? Can it be avoided?