Summary: Use a small amount of hot water, only bottom element comes on.
Use a lot of hot water, bottom first, then top, then bottom again, then off.
The lower element is supposed to come on first since the incoming cold water goes to (should go to) the bottom. If the top half of the tank is still hot the lower element will go off again when the bottom half is heated.
If you use so much hot water that incoming cold water gets near the top then the bottom element goes off and the top element goes on. Then when the top half is heated the top element goes off and the bottom element goes on. Finally the bottom element goes off when satisfied.
Are you sure that the top element consistently comes on first on your heater?
Are you sure you connected the thermostat correctly?
There are two thermostats, one near each element. The one on the bottom turns the power on and off. The one on top selects bottom element or top element. Except for some special purpose extra fast water heaters requiiring higher amperage circuits, both elements are not supposed to be on at the same time.
If you installed a new water heater and connected up the water backwards, that is connected the incoming cold water to the connection atop the tank labeled "hot" then nothing happens until the incoming cold water gets to the bottom. By this time the top of the tank is also cold and the top element comes on first. The performance of the heater is also poorer because this way there is a lot more commingling of hot and cold water within the tank since the cold water tends to sink.
Gas water heaters have just one thermostat, near the bottom. While all the heating takes place at the bottom where the gas burner is, a gas heater can heat the whole tankful in the time it takes the electric heater to heat just the top half.