The hot and cold water lines are connected together through the water heater. Water normally only flows one direction, from cold through the heater to hot, but (unless you have a check valve on the water heater's inlet) it can flow in either direction if the conditions are right. Hence, the air pocket in the water heater works on both the cold and hot water sides. Usually the only time there's a check valve at the water heater is in some setups where the bypass uses one or two valves rather than the straightforward three valve bypass setup.
I suspect that if you start with the water in the heater cold, and turn on the heater and let it warm up, and then open a cold water tap, the initial burst would be at a higher pressure than usual due to the expansion of the water in the heater when heating it.