I clean my filters by removing them from the tank and rinsing the media and just stacking it on a clean towel until I get it all clean and can return it to the filter. The media stays moist but is definitely exposed to air. On the other hand, I do not allow any of my media to become dry, that would kill off the bacteria. With 3 baskets of media, some of it is just somewhat moist when all is put back together but it means nothing and the filter starts working great as soon as all is put back in service. I water change my 125 gallon tank using 5 gallon buckets but only shut off the filter as it starts to lose suction. That way the filter keeps running most of the time. If it is time to clean that filter, I use the last bucket of water as my cleaning medium. Lugging 30 to 40 gallons of water down the stairs to the fish room takes a while but the bacteria always survive and thrive.
In your case you said you replaced carbon. Although the carbon is not intended to be a biological medium, it does part of the work. If you changed a large volume of carbon at once, you are probably in a mini-cycle. I would expect to see such an excursion finished in about a week unless you tossed an awful lot of your biological media as carbon.
Thank you! I also wait to unplug the filters until the water level gets too low, so I am pretty confident that the media doesn't dry out. I am still having to change the water once a day and the nitrate reading is is below 5 and this concerns me. Should it? Nitrites 0.