The finishing process is usually the longest part of a countertop project and it also requires a lot of planning to determine where, when and how you are going to complete the project. One important piece of the plan is what surfaces actually need to get finished. For some extensive planning help, check the Where, When and in What Order to Finish Countertops, but in general, it is a good idea to get at least some finish on all surfaces when possible.
Do I Absolutely NEED to Finish the Underside?
Typically, no. Finish is needed where protection is needed. The underside is generally not used, nor will there be standing water. If there is a situation where your surface will be exposed to lots of moisture or water (like an undermount sink), the entire finishing system should be applied in at least that area.
Should I Finish the Underside
If possible, yes. Wood is hygroscopic meaning that it will absorb and lose moisture as the environment changes. This can cause warping or other problems. Applying something to the wood tends to help regulate this moisture exchange and may eliminate or at least minimize any stresses or damage to the wood. This is not a guaranteed way to eliminate warping or other moisture problems, but it will only help.
Recommendation
It is recommended to apply at least one coat of sealer on all surfaces when possible. When using Waterlox product recommendation tools like the Find Your Finishing System tool or Find Your Application Guide, a sealer coat of some kind is usually recommended.
For buff-in products, like the Universal Tung Oil Sealer (UTOS) and the TrueTone Color-Infused Tung Oils, you can quickly apply a coat over the entire surface with minimal mess and minimal risks to the coating. Apply as directed and let dry for at least 2-4 hours before flipping.
For brush on products, it is best to finish one side and let it dry at least overnight before flipping. Always check for runs/drips immediately after application, especially with the wet applied products.
If your countertops are already installed, there is no major benefit to removing them just to put a coating on the underside.
As stated above, apply the full finishing system wherever there is a regular likely exposure to water. Most notable would be around undermount sinks. See the Finishing End Grain guide for some information on the end grain that may be exposed when installing an undermount sink.
Dishwashers are another logical concern due to the heat and steam that they can emit. Most dishwashers are usually well insulated and designed not to vent lots of moisture under your countertops so fully finishing the area over a dishwasher is not necessary. Some dishwashers will vent steam from the front door. These units usually come with (or recommend) a thin (6-8 inch) piece of moisture barrier tape for the front edge of the opening. Those should adhere fine to both finished and non-finished sections of the countertop and should be used when recommended by the dishwasher manufacturer. To summarize, it is not required to fully finish the underside of a countertop over a dishwasher, but there is no harm in doing so as long as you allow proper cure time (recommend 7 days) before sealing that surface off from any air flow. If possible, try to get one coat on the underside just to help regulate any humidity fluctuations.