Andrea, "PBIS" in public schools generally focuses on external "behavior" (The "B" in PBIS). But, if you've seen the "Trauma Iceberg" illustration, external behaviors are only the "tip" of the trauma iceberg.
Some will argue that "positive" approaches to behavior can be a step in the right direction, when compared to "zero tolerance" (for the most egregious behaviors) in public schools. But being better than "zero tolerance", is not part of the definition of trauma-informed.
Other will argue that PBIS is simply a manifestation of the "Behaviorist" world view. A manipulative approach with extrinsic incentives. Sort of like training a pet, using "treats".
Sometimes there seems to be short-term success with PBIS and younger students. Nevertheless, there is very likely no internal or intrinsic connection (best case) between the external incentive and the trauma experience which underlies the behavior.
Sometimes, in fact, the PBIS goals or 'norms' can backfire in a confined space, like a classroom, with students who have a history of certain trauma (restraint) experiences . So again, best case, trauma injuries are not directly addressed via a focus on external behaviors.
Meanwhile the overriding importance of healing-in-relation (especially from relational trauma) and the deeper change via intrinsic motivation are often discounted or ignored in the focus on a PBIS "system".
My "two cents" of perspective from the front line....