Suppose a particular neurotransmitter causes an ipsp in postsynaptic cell x and an epsp in postsynaptic cell y. A likely explanation is that

This situation states that the cells has two different receptors on them.

Explanation:

The particular neurotransmitter can have different receptors on them. An (EPSN) excitatory postsynaptic potential causes change in the membrane potential of the postsynaptic cell which tends to open the channels for the positively charged ions inside the cell.

This leads to the activation of the ligand sensitive channels.

In case of the inhibitory postsynaptic potential ( IPSP) makes the neurons less like to generate any action potential.

So, for the same neurotransmitter, one cell X shows excitatory response and other cell y shows inhibitory response.