Why aren't DM's showing in the Request section of Twitter being created as tickets?
DMs under the Requests tab don't create tickets because those requests are messages sent by people who don't follow you on Twitter. Until you approve the message, it does not show up in your inbox. Zendesk Support only creates tickets from DMs that reach your inbox, that is, from people that you've accepted to follow your account or from message requests you've approved.
The Twitter article About Direct Messages goes into further detail:
If you have the Receive messages from anyone setting enabled, incoming messages from people you don’t follow will appear as requests in the Messages tab. New group conversations that you’re added to by people you don’t follow will also appear in Requests. Entering the conversation, you will be asked to either delete or accept the message. Accepting the message will allow you to engage with the person, and will move the message to your inbox.
Once the DMs move from Requests to your inbox, the tickets are created in your Zendesk account.