Yes it is possible that if both units are connected by the same cold water line that when your neibour shuts off their cold tap then the vibration will bounce back and be heard on all connections to that line. This is called water hammer and is mainly due to pipework not being clipped or strapped correctly or the holes in the timber through which they pass are too loose allowing the pipework to rattle around. No simple fix unless you can get to the pipework in the first place to secure it from rattling about in the first place. There are devices called water hammer arrestors that can be fitted to the inlet cold water lines to assist in overcomming this problem. Fast opening solenoid valves on some washing machines etc can also cause the problem for when they shut they actually slam shut fast causing a shock wave to pass back through the water piping making the vibration noise. Hope this helps.
Selgas Services Ltd
Craftsman Gasfitters, Plumbers, Electrical Service Technicians