There are two things to check to ensure more than Twitter data can be pulled.
First is to check the ruleset in the Edit Monitor. Make sure that no rules have been added to restrict which networks are being pulled.
Note: By default, all networks will be pulled.
Second, if you have run a historical job, it will only pull Twitter data. A lot of confusion comes from what is pulled for Historical Jobs, but it is only on Twitter.
Also to confirm the networks, check the Trending Networks graph located on the monitor's overview page.