Does Theravada posit the selflessness of phenomena?
The Vaibashika school doesn’t assert the selflessness of phenomena
  because they hold the view that phenomena is truly existent from its
  own side.


In my opinion, the Theravada view according to the Pali suttas imply that:


The self (of persons) is not truly existent.
Whether non-self phenomena are truly existent from its own side or not, is (probably) not important towards the path to the end of suffering. (See the Parable of the Poisoned Arrow, Parable of the Simsapa Leaves and the Discourse on the Unconjecturables)


Of course, there may be a lot of Theravadins out there who dispute my second statement above, and would assert that all non-self phenomena are truly existent from its own side.

EDIT: Just to make it clearer:

All sankharas (conditioned and/or compounded things) are subject to change, arising and passing. Nibbana is not subject to change, arising and passing. Both sankharas and nibbana are empty of a self. But this does not mean that sankharas and nibbana are not truly existent. The self is definitely an illusion, but the world, transient as it is, may not be an illusion. Whether the world is an illusion or not, is not important to the path to the end of suffering (according to Theravada, in my opinion).