With regards to humidity, I seem to have the opposite intended effect in my basement when my central A/C is running...
I live in Maryland and have a 1960s Cape Cod style home with an unfinished basement, mostly below grade. Moved in recently, so I'm still getting a feel for all the nuances.
I have a dehumidifier set to 50% in one-corner of the basement that feeds into the sump pit. I have a smaller dehumidifier in the opposite corner set to 55% (just in case) -- I kind of keep it around as a backup. In the middle of the basement, I have a hygrometer that has read 46-50% in the Spring with this setup. Perfect.
I have recently noticed that when the central A/C is running, the humidity at the first-floor thermostat lowers nicely... but the basement humidity steadily ticks UP. The dehumidifier combo can't keep up. I've seen the hygrometer climb toward 60% already and it's not even hot yet. Any temperature change in the basement is negligible. When the central A/C fans kick off.. the basement humidity lowers as the dehumidifiers work... It is a constantly push/pull.
I don't see any open registers in the basement.. only a weighted damper of some kind which I'm not familiar with.. it appears to stay closed.
I initially thought that the exposed ducts were lowering the temperature in the basement, thus raising the relative humidity... but I'm not sure this is the case. It seems moisture is being introduced somehow. Is the system pulling outside moisture from the basement walls and windows?
More Info (Added Later)
My condensate line pumps into the sump pit... I haven't seen any noticeable leaks or puddling, but I will check again.
However, the changes in humidity % are pretty sudden.. and the central hygrometer is 15 feet or so from the fan... given that, unless it was a major water issue, I have to imagine this is an air or temperature-based phenomenon.
After messing with some online calculators.. it's not hard to jump 5% in humidity... decrease the temp by 1 degree and increase the dewpoint by 1 degree and you've basically done it. I bet the air leaks and the exposed ducts are probably the culprit.