In this work we consider the problem of control under Signal Temporal Logic specifications (STL) that depend on relative position information among neighboring agents. In particular, we consider STL tasks for given pairs of agents whose satisfaction is translated into a set of setpoint output tracking problems with transient and steady-state constraints. Contrary to existing work the proposed framework does not require initial satisfaction of the funnel constraints but can ensure their satisfaction within a pre-specified finite time. Given a tree topology in which agents sharing a STL task form an edge, we show that the resulting control laws ensure the satisfaction of the STL task as well as boundedness of all closed loop signals using only local information.