Puffing occurs whenever a dough with sufficient air bubbles is heated rapidly. In this regard, a pita in not different than any other hearth bread baked at high temperatures. Letting the dough raise after rolling lets new air bubbles be created as an insurance against access degassing at the rolling stage.
The thinner the pita is rolled, the more distinct the pocket will be. Roti is on the extreme of this spectrom - rolled very thin so that after puffing it collapses into two thin layers. A good pita (of the kind I associate with the word the most) should not be rolled too thin. This allowes the pita to have fluffy and bready "walls" rather than papery ones. Hand pressing it as thick as one whould shape a pizza crust is the way to go.