Multitasking support requires the app to target iOS 9.0 SDK (with a couple of checkboxes), and no one can submit apps with such target so far. For the record, the current version of Twitter is not yet eligible for the multitasking view.
Many of the "iOS 9 supports" you can see now are mostly those that have no business of new stuff in iOS9 (i.e. just fixes for bugs and layout on iOS9), or somehow they worked it around despite being at a lower version of SDK target, e.g. Twitterrific's use of Safari View Controller.