This is one of those questions that, if posed to 10 chicken keepers will likely yield 11 different answers, lol. Eggs can be kept at room temperature until they are used - never seeing the inside of a refrigerator; eggs can also be immediately cleaned and put in the fridge - or they can be left out, then cleaned and refrigerated. The key is *if* they are cleaned (washed) they must be refrigerated - if they are refrigerated they should then be kept refrigerated (vs. refrigerated, then put on the counter).
I only clean my eggs if they are extremely dirty (this is rare as I use my management approach to avoid hen's with dirty feet and/or waste in the nest boxes). Most often, if an egg requires cleaning I will do it right before I wish to use the egg or before it is packaged to go out the door. It is not uncommon for eggs to sit on my counter for a day or two prior to being cartoned up and put in the fridge, sometimes the eggs I intend for our family's use never get put in the fridge.