I've seen inconsistencies in the pH, but there are so many factors that affect it that I'm not always sure what is the cause. I have noticed that pulling outside air for the skimmer definitely raised the pH overall - both the upper limit and lower limit. So that would suggest the opposite of what you're seeing.
I recently added CO2 scrubber to the air intake for the skimmer as well, and that brought it up even further. On my tank, the 3 biggest influencers of pH are the skimmer, the lighting, and the ambient CO2 levels. Obviously when the lights are on, CO2 is being consumed by the photosynthetic creatures so the pH goes up. If the skimmer isn't working efficiently, the pH goes down - sometimes a LOT. If the CO2 in the house goes above 1000ppm for a while, then sometimes the tank's pH will start to go down.
Interestingly if you are seeing the pH go down when the pump is on, then perhaps it's getting stale air? Is it well ventilated where the pump it?
Here's my charts.