It seems to depend on the size of the neurotransmitter. The bigger the neurotransmitter is the longer the neuron has to be stimulated to actually release the neurotransmitter. But in the case of Acetylcholine it seems to need only about 2ms after a presynaptic stimulus to generate a postsynaptic membrane potential and after about 5ms all the Acetylcholine in the synaptic gap is cleaved allowing the postsynaptic cell to repolarize. The example get described here.