If the valve is meant for controlling pressure upstream of the valve (pressure sustaining/ maintaining type), it will close but if it is controlling pressure downstream of the valve (inline throttling type) it will open up. The converse is true if pressure increases above setpoint.
The application I am familiar with is where we have used these valves to control the fire ring main at 11 bar. On both ends we have had these self-controlled pressure relieve valves installed and once the fire pumps have started, actuated automatically by a pressure switch, the pressure in the ring main will go to high and one or sometimes both these pressure controllers will open up proportionally in order to keep the pressure at 11 Bar. In other words the higher the pressure difference between the set pressure and the upstream pressure the more the valve will open up. So the ring main will be the upstream pressure and the overboard dump line will be the downstream pressure and the set pressure is the 11 Bar set on the valve. Obviously when the upstream or ring main pressure gets closer to the set pressure, the valve will close proportionally and once it is equal to the set pressure the valve will be closed. So you can see for yourself that if the pressure on the upstream side is below the set pressure the valve stay close and will only react on a upstream higher than set pressure.
