In cabin pressurisation systems, I thought that the negative relief valve is automatically opened if outside pressure becomes greater than inside pressure.
The positive pressure relief valve opens in case the cabin pressure is too high in comparison to outside air Pressure. This happens if the pressure differential is higher than 8.85 psi / 0.61 bar (Airbus). It is most likely to happen in malfunction of the outflow valve (stays closed).
The negative pressure relief valve opens most likely during descent, when the cabin altitude is still at 8,000 feet (normal condition) but the aircraft itself is lower than that. That means that the pressure outside of the aircraft is higher than inside. The valve opens at a differential pressure of -1 psi / 0.07 bar.
Aircraft are built to withstand higher pressure on the inside without damage -- think of blowing up a balloon without it popping -- but there is a limit to how much pressure they're designed to take. Thus the positive pressure relief valve opens if the pressure inside becomes greater than desired, so as to keep if from reaching the point where damage could occur.
On the other hand, the aircraft are NOT designed nearly so robust as far as pressures outside being greater than pressures inside go -- think of the "crushed can" demonstration in science class. It's rare that this occurs, mainly because digital pressurization controllers are pretty smart, but under the right (wrong!) circumstances, it's not impossible. Having greater pressure outside the fuselage than in it is considered "negative pressure" and that's a bad thing... thus the negative pressure relief valve opens at a far lower differential than the positive pressure relief valve.