Hi, clark. I'll take a guess but without looking at your system, it is only a guess.
Most valves control only flow volume, not pressure. The water pressure that you have in your house is the same that is in the city water system. However, there are some inlet valves that do regulate pressure also. These are normally installed only where you have city water at pretty high pressure and can be adjusted to control the pressure in your house plumbing so the pressure does not "overload" the system and you have leaks everywhere.
The pop valve at the top of your water heater opens when a maximum pressure has been reached. This is necessary in case your water heater heat source (usually a gas flame) stays on. If this happens, your water heater can turn into a boiler and can explode. But the pop valve opens to release the pressure so it does not explode. Do not try to adjust this valve. It is preset at the factory to a safe level.
If you turned up the pressure to all the plumbing in the house, it could have been enough to open the pop valve and let water escape out the drain pipe on the side. Adjusting the pressure maintaining valve where the water comes in from the city mains should resolve the problem and you or your landlord should have a gauge to do that.
You probably did not do any damage to your water heater, but you did make a mess in the basement. Hopefully, you have a floor drain pretty close to the water heater and most of the water ran down the floor to it. The most important thing now is to get everything dry or mold and mildew could become big problems. If you have wet carpets in the basement, you need to get them outside (like in a garage) to dry.