"in a chemical synapse, neurotransmitters are spilled into the synaptic cleft by what action? "

Starting from the triggering action potential, the membrane potential in the neuron will propagate from the dendrites to the cell body then to the axons where synaptic vesicles are located. The action potential will trigger an influx of calcium into the axon then calcium will bind to proteins that will move the synaptic vesicles to the synaptic cleft. The membrane of the synaptic vesicles will eventually join the membrane of the synapse and then the neurotransmitters inside the vesicles will be "spilled" into the synaptic cleft.