Cedar is very durable to changes in moisture. The trays have not been treated with anything and won't need any treatment. The main thing to keep in mind is to allow the trays to air out after use before putting them away in an area with little air flow.
Spoons and Other Utensils
All of the utensils that I make are wiped down with walnut oil. Walnut oil is one of several natural "drying oils", but is the one that I find to be the most easily accessible and most economical. For lasting durability, I recommend you purchase a bottle of walnut oil, or others such as food-grade linseed oil (not boiled) or tung oil.
Drying oils polymerize on the outside of the wood, effectively creating a seal around the utensil. With heavy use, the polymer coating on the outside could get worn off. If so, just reapply walnut oil. Pour some oil on a paper towel and wipe down the spoon or utensil. Allow the oil to soak in for five minutes, and then wipe dry.
Hand wash all utensils without soaking. Just wash, rinse and then dry.