Of course it only makes sense to apply a static evaluation function to a position which is quiescent, or tactically quiet. As a result, the tree is extended beyond leaf nodes until a quiescent position is reached, where the static evaluator is actually applied.
We can think of the quiescence search as a dynamic evaluation function, which takes into account tactical possibilities. At each leaf node, the side to move has the choice of accepting the current static evaluation or of trying to improve its position by tactics. Tactical moves which can be tried include pawn promotions, most capture moves, some checks, and some pawn promotion threats. At each newly generated position the dynamic evaluator is applied again. At the nominal leaf nodes, therefore, a narrow (small branching factor) tactical search is done, with the static evaluator applied at all terminal points of this search (which end up being the true leaves).