The synaptic drive from neuronal populations varies considerably over short time scales. Such changes in the pre-synaptic rate trigger many temporal processes absent under steady-state conditions. This paper examines the differential impact of pyramidal cell population bursts on post-synaptic pyramidal cells receiving depressing synapses, and on a class of interneuron that receives facilitating synapses. In experiment a significant shift of the order of one hundred milliseconds is seen between the response of these two cell classes to the same population burst. It is demonstrated here that such a temporal differentiation of the response can be explained by the synaptic and membrane properties without recourse to elaborate cortical wiring schemes. Experimental data is first used to construct models of the two types of dynamic synaptic response. A population-based approach is then followed to examine analytically the temporal synaptic filtering effects of the population burst for the two post-synaptic targets. The peak-to-peak delays seen in experiment can be captured by the model for experimentally realistic parameter ranges. It is further shown that the temporal separation of the response is communicated in the outgoing action potentials of the two post-synaptic cells: pyramidal cells fire at the beginning of the burst and the class of interneuron receiving facilitating synapses fires at the end of the burst. The functional role of such delays in the temporal organisation of activity in the cortical microcircuit is discussed.