Basement Humidity Increases When Central A/C is Running
It's pulling air from outside

When the A/C starts, it's somehow pulling more humid air from outside into the basement. Hot air can hold a lot more humidity, so on a hot day, outside air that is below 50% relative humidity enters your cold basement and becomes air that is over 50% relative humidity.

Since the basement is cool already, decide whether you want the basement as part of your AC envelope, and if so, duct and seal accordingly. As you know, AC already dehumidifies, so running a dehumidifier alongside it makes no sense.