is it possible to have a unstable water pressure?
Yes very possible to have erratic pressure that can cause leaks that appear during spikes. 

This is why a pressure regulating valve should be installed in between municipal water tap and the house.

Ask your apartment manager to verify that such a regulator is in place and that it is functioning properly. 

These valves can and do go bad over time and should be replaced to prevent the type leaks you are describing. 

Typically the highest pressure in a municipal water system will occur during the time when fewest numbers of citizens are using water. Late at night when everyone is asleep.