Yes your understanding is correct. He also suggested if we do separate grounding the issue will be fixed. But my concern here is what if one of the 4 ground wires, belongs to my house? I want to test before going for separate grounding which will be expensive for sure cause need to buy thick copper wires for earthing. One way to test is to disconnect the 4 faulty ground line and then check each house but sadly we didn’t have the multimeter and I have placed an order in amazon. Once i get the multimeter I will remove the faulty line and test. The electrician suggested two options. One is to do a separate line for me with individual grounding. Next is we need to bring a carpenter to remove the cupboard and also involve EB to disconnect the power and then check the wiring behind the cupboard. The meters and switches are installed outside the cupboard with all the wires behind the cupboard.I don't know what he did to fry the multimeter. Most probably he had selector in wrong position. Sad.
If I understand it correctly, he disconnected the earthing from from each apartment coming to the earthing strip at the ground level. Then he connected one probe of the bulb to the main neutral wire and checked earthing wire coming out of each apartment using the other probe. In that case there was no wire going to the ground right? It's just an wire coming out of each apartment,which is not connected to earthing.
In that case bulb should not glow at all as there is a open circuit unless there is leakage from live wire to the body of the appliances. It looks like three is leakage in 4 houses. One way to check is turn of the mains to those 4 houses and check again.
Did you check the color of copper wires while disconnecting. If there was huge leakage, the wire gets charred and brittle.
If you have option to get a separate earthing done for your apartment, that's a better option in my opinion. You will be saved from such stray leakage from other people's appliances.