My purchase was in April, not after July 1st, and my purchase price was below $35,000. That said, I contacted the Department of Revenue and acquired all the details before I made my purchase. I reviewed the details with the dealer's finance/licensing people, to make sure they understood.
It was the Department of Licensing that required a little extra documentation. My purchase might have struck them as a little odd: I purchased the car out of a dealership in Beaverton, Oregon, and had the licensing done through that dealership's Vancouver, WA partner (a GM/Cadillac dealership in Vancouver). The Department of Licensing required a copy of the original window sticker, to complete the transaction.
In the end, though, the sales tax exemption worked perfectly. I'm a resident living in unincorporated Thurston County and ended up paying less than $20 in taxes. I cannot at this moment recall which taxing district was not included in the exemption.