This is a matter of understanding psychrometrics.
I am going to make an assumption here that you are measuring the relative humidity.
If you close the windows and turn on the air conditioner you drop the temperature within the space. When you drop the temperature within the space the relative humidity rises.
This means that the ability of the year to hold moisture is reduced. That is because the air conditioner reduces the temperature below the dewpoint and subsequently reduces the water vapor in the air.
If you repeat that same air without opening the windows, you will end up with a relative humidity of about 10% (depending on how high you raise the temperature.
There is absolutely nothing wrong with what you’re describing.
That’s how air-conditioners work!
There is nothing to suggest.
A dehumidifier is nothing but an air conditioner that discharges the hot compressed air back into the house and raises temperature.
If you’re going to take psychrometric readings with a hygrometer, I highly recommend that you brush up and hit the books and learn about psychrometrics.