"However, am trying to determine whether or not the plumber who installed the water heater simply mixed up the lines when attaching to the water heater tank."
If the lines are reversed now, then the plumber mixed up the lines. The only way to tell is to look at the heater and see which is connected at which label. Are we missing something here?
The labeled cold water inlet is connected to an internal "dip tube" that extends to the bottom of the tank. The hot water comes out from the top.
Because cold water is more dense than hot, the water tends to stratify with hotter at the top and colder at the bottom.
The controls of the heater are set to give the top element priority so that when the water is below the set temperature, that water is heated. The lower control is often set a little lower than the top control.
If you reverse the flow from the way the heater is designed, then the cold water comes in at the top and hot water is drawn from the bottom. Since the heating priority is at the top, you don't get as much hot water as you should.