Shouldn’t that fire an alert of some sort that the system is having to work at higher capacity than normal to maintain pressure for the current altitude?
On a modern airliner, you'll get an alarm when the cabin pressure exceeds the pressure equivalent 10K feet. A few thousand feet of cabin altitude higher and the rubber jungle of masks appears. You won't get an alarm for just cabin pressure differential begin lower than usual.
So the air conditioning system essentially runs at a fixed capacity (although some very modern aircraft with electric compressors may vary). Pressure is regulated by controlling the amount of air exhausted by the cabin outflow valve near the back of the airplane.
Since they're are so many variables that can go into the inflow and outflow rates it's unlikely that anybody had characterized outflow valve position in all possible conditions. Nor is it's specific position of any concern, just that it be in the right position to maintain the selected cabin pressure.
So no, it's unlikely that they're would be an alert attached to its position, what is however likely is that they're is an alert to warn that cabin pressure has deviated from the commanded pressure. In this case though they never found themselves in a position where the aircraft was unable to regulate cabin pressure.