A public tweet containing your Twitter account's user name did not automatically create a ticket.
Confirm that your Twitter channel in Zendesk is configured properly to automatically convert public mentions to tickets. If your Zendesk account is not configured to capture public mentions, then it is expected that the tweet doesn't create a ticket.
If all new public tweets containing your Twitter account user name are not converting to tickets, re-authorize your Twitter account with Zendesk by deactivating and reactivating the account. For more information see this article: Removing Twitter accounts from Support.
If you would like quote tweets, a retweet with an added comment, that include public mentions to be converted to tickets, contact Zendesk Customer Support.