Building upon what @Joe already mentioned.
The cheesecake rises because as the temperature of the air trapped inside the mix goes up it tends to move upwards. This creates an effective spring force pushing the mix up. The hotter the oven, the stronger is the force since the bigger is the temperature gradient between the air inside of the mix and the top of the oven.
This phenomenon is sometimes called oven spring, especially among bread bakers (which by the way go crazy trying to maximize it!). As your mix cooks, it loses elasticity and become rigid. In the case of the cheesecake, this is mainly due to the coagulation of the egg proteins. Thus the oven spring effect takes place mainly in the initial cooking stage.
Different from bread bakers, you want to minimize this effect. The key for that is to have the eggs cooked with the least temperature gradient between the center of the mix and the top of the oven. Egg coagulates at around 70 degrees, so you don't really need high temperatures to make the cheesecake set.
One simple but laborious approach would be to start cooking the cheesecake at lower temperatures and only after it has set you to increase it to get browning on the top. One way of checking this is to shake it and see if the top moves or not, or to drill it with a toothpick. The water bath also helps to reduce the speed in which heat penetrates the mix since it effectively 'shields' the cake with a layer which has higher heat capacity.