First, it's a use tax not a sales tax, I believe they are the same rate but a sales tax is collected by the seller and turned over to the state a use tax is paid by the buyer after the fact. For people who live on the southern border of the state and make purchases in Oregon where there is no sales tax they are supposed to fill out a form and pay a use tax on any items they bring into the state and plan on using. This doesn't often happen but just trying to layout what is technically legal and what the correct terms are.

Next, you are supposed to get tags/registration transferred within 15 days of becoming a resident in Washington, there is an extra fee associated with registering your vehicle after the 15 days are up. I recently registered a vehicle I purchased that was registered out of state and was told that they will often waive the 15 day requirement for out of state vehicles as long as it is still registered promptly, but this sounds like it is up to the discretion of the individual agent processing the transaction, my registration was made 17 days after the bill of sale as we had to wait for the finance company to mail the title.

You say you purchased the vehicle in 2018 while living in another state and moved to Washington around the same time the vehicle was paid off and only recently received the physical title. If that is the case you should bring the bill of sale with you to your county DOL as well as the title, you may have to pay the extra fee for failing to register within 15 days, but as you owned the vehicle more than 90 prior to moving to Washington you should not have to pay a use tax as you purchased the vehicle in 2018.

The use tax if paid is based on the value of the vehicle, they will accept the purchase price as the value as long as it is a reasonable number, so a purchase price of $10k on a $35k vehicle is going to be taxed at $35k, but buying a $15k vehicle for $13.5k is going to be taxed at $13.5k unless you piss off the clerk and they have reason to investigate the value. I say this because I just purchased a vehicle that blue booked for $14.5k and I paid $11.2k and was only taxed at the $11.2k rate.

My suggestion is to just go into the county DOL office and explain everything you can to them and if something doesn't seem right as them to explain why they feel you should pay a fee or tax. It is possible based on your story here there is a miscommunication and they think you just purchased the vehicle in August when it was really purchased by you in 2018 and you are only registering now because you moved and paid off the vehicle around the same time. Also if they still make you pay a use tax bring whatever purchase paperwork you have as any sales or use tax that has been previously paid by you can be credited against any use tax you may owe.